Low Cost, Student Slide Rules   Cheap, Low Cost, Student and First Slide Rules! This Section Updated WeeklyClick REFRESH on your browser if pages seem unchanged Please Note:All Prices are in US$Sphere Research Corporation3394 Sunnyside Rd.West Kelowna, BC, Canada V1Z 2V4Phone: +1 (250) 769-1834 A great source for test equipment, repairs, calibrations, useful metrology information, and of course, SLIDE RULES!Want something? e-mail us!Our FAQ !! Answers to all those questions.Visit our amazing document server. Quotes & SciFi to Ethics & Business. Just SCROLL DOWN to see everything!  Click to See What's NEW...... Welcome to the Slide Rule Universe! CLICK HERETo Visit The S/R Marketplace  I'm in a HURRY! Show me all the: NIB Rules NIB Pickett Rules Pocket Rules Circular Rules FREE stuff!  The Slide Rule UniverseClick to VISIT or RETURNClick Here To go back to the Slide Rule Marketplace Marketplace Navigation Go to the Auction Page Go to the Slide Rule Books Cheap Slide Rules Go to the Circular Slide Rules Go to the -NEW- Drawing &Measuring Tools Go to the Exotic Slide Rules Marketplace Navigation Go to the Full Sized Slide Rules Go to the New In The Box Slide Rules Go to the New-In-Box PickettSlide Rules Go to the -NEW-Pins and Tie ClipSlide Rules Go to the Pocket Slide Rules Go to the -NEW-Slide Rule Cases Go to the Slide Rule Parts Marketplace Navigation CHEAP / STARTER / STUDENT SLIDE RULES CHEAP / STARTER / STUDENT SLIDE RULES Skip the INTRO, Go RIGHT to the CATALOG! To make your life easier, and help you find exactly what you want, we have broken the on-line slide rule catalogs into smaller sections. Just CLICK on the icon of the rule type you are looking for at the left, to see the matching catalog. Large graphical catalogs are a bit SLOW, please give them time to load. You can order anything here just by picking up the phone, and calling (250) 769-1834 during normal office hours, 8:30AM to 4:30PM PST. OR, Email your order to Susan HERE. SHIPPING: Preferred and Alternate Methods as of June 4, 2013, CLICK for FULL DETAILS ON OUR FAQ Page. Rates are now changing rapidly, often with little notice to us, so all the data has been transferred to the FAQ page for speedy updating. E-Mail Susan if you want a quote for shipping to other destinations, or for something heavy. Sorry, we can't safely send most individual small parts in a regular letter envelope, they get destroyed by the automated handling equipment. Sometimes we can ship very rugged parts or plastic body pocket slide rules in a small padded envelope by letter post. Ask Susan. If we have your valid data on file, you can just click on the ORDER email link to place an order and indicate your approval to bill, and we will do the rest. We keep your active information for ONE YEAR for your convenience. If this is the first time you have dealt with us, you can phone +1 (250) 769-1834 to supply the billing info, or send it by the email link, as you prefer. We accept VISA/MC, international money order, Paypal (to Susan@Okanagan.net), and bank wire transfer. Please note that there are transaction fees with Paypal and wire transfer payments, the wire transfer fee is frankly horrifying. We scoured the world looking for inexpensive slide rules for learners and classes, and came up with a large quantity to pick from. These are almost all NEW sets, note there are a few which have been used previously, but are in excellent condition. TEACHERS, do you need inexpensive rules for classes? We have stock set aside for this purpose, and offer it at reduced prices. EMAIL SUSAN HERE if you need help with this purchase, and have limited or no funding. The CATALOG will appear below shortly! CATALOG:JUST SCROLL DOWN TO SEE EVERYTHING ! SEE THE POCKET SLIDE RULE PAGE for more lower cost small rules! SLIDE RULE INFO / SCALES QUANTITY PRICE EA. STERLING PRECISION 585 10" Deluxe Mannheim Rule CLICK for BIGGER PIC CLICK for BIGGER PIC CLICK for BIGGER PIC 12" / 10" plastic body Slide Rule LATE MODEL, made by Sterling (later Borden which bought out both Acumath and Sterling Plastics, and continued to sell under those names). Includes instructions, black engraved and filled scales, and green contrasting color slide (some have green bodies, it is random). We also have some all white, with RED inverse scales, and a blue slip case. Has 2 side rulers (1/16 and 0.050 inch), plus trig scales on the slide reverse, with a plastic sleeve case and illustrated instructions. An inexpensive and practical first or student rule, made in USA. You can have your choice, both are the same rule other than colors. (9 Scales) Front - Inch/ A, [ B, CI, C, ] D, K, \Inch Back - [ S, L, T ] CLICK for Bigger Pic! Have 4 Green Have 5 White Includes: Case Rule Instructions US$22

Sterling 585
Like this rule?

CLICK TO ORDER

SLIDE RULE
INFO / SCALES
QUANTITY
PRICE EA.
STERLING PRECISION
589

10" Senior Mannheim Rule

CLICK for BIGGER PIC

CLICK for BIGGER PIC

12" / 10" plastic body Slide Rule
LATE MODEL, made by Sterling (later Borden which bought out both Acumath and Sterling Plastics, and continued to sell under those names). Includes instructions, black engraved and filled scales, and green contrasting color slide. Includes a plastic sleeve case and illustrated instructions. An inexpensive and practical first or student rule, made in USA.

(9 Scales)

Front A, [ B, CI, C, ] D, K
Back - [ S, L, T ]

CLICK for Bigger Pic!
Have 8

Includes:

Case
Rule
Instructions

US$18 Sterling 589 Like this rule? CLICK TO ORDER SLIDE RULE INFO / SCALES QUANTITY PRICE EA. STERLING PRECISION 651 10" Metric Converter Rule CLICK for BIGGER PIC 12" / 10" plastic body Slide Rule LATE MODEL, made by Sterling (later Borden which bought out both Acumath and Sterling Plastics, and continued to sell under those names). Includes instructions, black engraved and filled scales, and yellow contrasting color slide. Can do 16 metric conversions from US standards to Metric units and vice versa. Front slide for distance and area, reversible slide for weight and volume conversions. An inexpensive and practical rule for any science students, cooks, or anyone needing to work in both unit systems. Made in USA. (16 Conversions) Front - [ Inches/cm, m/feet, m/yards, miles/km, sq. in./sq. cm, sq.m/sq. ft x10, sq. m/sq yards, sq. miles/sq. km ] Back - [ cu. in./cu cm x10, cu m/cu.ft.x10, cu. m/cu. yards, l/qt., oz./g x10, kg/lbs, metric tons/short tons, gal./l] CLICK for Bigger Pic! Have 25 Includes: Case Rule Instructions US$19

Sterling 651
Like this rule?

CLICK TO ORDER

SLIDE RULE
INFO / SCALES
QUANTITY
PRICE EACH
2-Rule
Super School Pack

27401-X

CLICK for BIGGER PIC

CLICK for BIGGER PIC

27103

Click for bigger PIC!

CLICK for OTHER SIDE

 Super School Pack, CLICK for bigger PIC! Quantity is limited! A great learning package.

Full Size and Pocket Size Educational Pack
VERY LATE MODELS, BRAND NEW, Every year we try and come up with an inexpensive but high quality school set for students wanting to learn about slide rules. This year, thanks to a one-time buy in Peru of all places, we are able to provide an amazing set of both full size 27401-X and pocket sized 27103 BRAND NEW Logarex/Koh-I-Noor Trig slide rules, complete with cases and printed instructions AND a free learning pack created by the good folks at the Oughtred Society to make it possible to fully master slide rule operation on your own, or in a class setting. Both rules feature data references on the back side. The pocket rule also features both inch and cm rulers - incredibly handy! Both rules are self-documenting, with actual values (X, 1/X, etc.) rather than just random scale names, great for fast learning.

The Oughtred Society educational items (over 150Mb) are provided on a mini-CD (works in a standard drive). For those with no suitable drive, web links are provided to download the PDF files directly to your device via the internet. This package also includes a basic printed slide rule manual in Spanish that comes with the pocket rule, and a brochure on the Oughtred Society so you can join to learn more about slide rules. By keeping the size and weight down we can also offer FREE shipping anywhere on earth for this deal only (off-world too, if you provide the carrier details), so don't miss out on this one time special. The one price is all you pay to get it sent right to your door (typically 2 week delivery, faster Expresspost delivery is available for an additional charge).
Free Oughtred Books Included:

(Full Size Rule - 10 Scales)
Front - K, A, [ B, CI, C, ] D, L
Back - [ S, ST, T ] + Data

(Pocket Size Rule - 9 Scales + 2 Rulers)
Front - K, A, [ B, CI, C ] D, L
Back - inch [ S, T ] cm + Data

Customer Feedback on this Pack:
Years ago in the 90s my father looked for a slide rule in a high street shop forgetting they were obsolescent since the mid 70s. Finally I found one for him at Slide Rule Universe and immediately enquired as to range of items, pricing and postage. The response was immediate and professional and the service superb. Within days I had a slide rule and manual shipped from Canada to my father in Hong Kong and it made his day. Thanks again to Susan at Slide Rule Universe and I shall definitely be a repeat customer.
--Eugene Daniel, UK
last 15 Sets

Includes:
27103 Set
27401-X Set
CD Books
Manuals + Reprints
Shipping

$69 ea. Shipping Included! Super School Pack Like this rule? CLICK TO ORDER SLIDE RULE INFO / SCALES QUANTITY PRICE EACH Logarex KOH-I-NOOR 27401-X Reitz-Enhanced 10" Rule CLICK for BIGGER PIC CLICK for BIGGER PIC Scale Close-Ups  CLICK for bigger PIC! CLICK for bigger PIC! Just got lots more in for class sets! 12" / 10" plastic body Slide Rule VERY LATE MODEL, MINT CONDITION. NEW, mint condition Logarex/KOH-I-NOOR sets with 2 part green plastic case. Basic Rietz format rule (has over-range scale extensions for easier operation) with added reference features. It has a black/red self-documenting scale arrangement and pale yellow slide. The slide reverse has trig (S, ST, T) scales, and the back has a treasure trove of useful data and factors. It has a slightly magnifying multi-line simplex cursor design that does area of a circle, plus some other interesting stuff like horsepower conversion. These are beautifully made rules, very well constructed. We will include basic instruction reprints, as these came bulk packed with with no manuals. Made in Czechoslovakia, they were marketed world wide under the KOH-I-NOOR brand. We got the chance to make one big purchase of these, no more when they are gone! Great starter rule for older kids! (10 Scales) Front - K, A, [ B, CI, C, ] D, L Back - [ S, ST, T ] Powerful low cost rule, loaded with features, great value! Have 129 Includes: Rule Hard Case Manual Reprint Now only$39 Ea.

Logarex/KOH-I-NOOR 27401-X
Like this rule?

CLICK TO ORDER

SLIDE RULE
INFO / SCALES
QUANTITY
PRICE EA.

DIETZGEN
MANIPHASE
1768-P

CLICK for BIGGER PIC

An excellent quality, visually attractive single sided student rule from Dietzgen.

12"/10" Maniphase Slide Rule
BRAND NEW, factory bagged, complete with manual. Plastic body rule with green colored slide and end braces, self-documenting on the right hand side. Includes trig scales on same side as other scales. Mint condition, and the last ones we can get.

(9 scales)
Front - K, S, A, [ B, CI, C, ] D, T, L
Back - Blank

Add a new Sphere case to make a complete set, $79 complete! Want to know more about our NEW SPHERE CASES? JUST CLICK HERE! Last Set Includes: Manual$49

Save $10 1768-P Like this rule? CLICK TO ORDER SLIDE RULE INFO / SCALES QUANTITY PRICE EACH 9 Scale Rule CLICK for BIGGER PIC CLICK for BIGGER PIC 6" / 5" Pocket Simplex Slide Rule VERY LATE MODEL, BRAND NEW, Embossed white plastic construction, filled black scales with edge inch and metric rulers, very handy! Has SLT scales on slide reverse for logs and trig functions. This is a great low cost pocket rule, admittedly generic in nature, probably from Japan in the 60's or 70's, but has no maker's marks at all. We get many requests for this kind of rule, always hard to keep in stock. Please note, we will provide a Pickett reprint that works with this rule. Just got one more batch, they will go FAST at this price! A great stocking stuffer! One rule CAN ship in a first class padded envelope for$6 if you feel brave. PLUS, we now have nice dark blue leatherette slip cases susan just made for these, add $5 each. (9 Scales + 2 Rulers) Front - cm/ A, [ B, CI, C ] D, K \in Back - [ S, L, T ] Still NEW bagged with reprint! GREAT FEATURE! The CURSOR can't get lost, it's locked on the rule! Have 99 Includes: Reprint Sheet$18 Ea.

9 Scale Rule
Like this rule?

CLICK TO ORDER 9 Scale Rule

SLIDE RULE
INFO / SCALES
QUANTITY
PRICE EACH

6 Scale Rule

CLICK for BIGGER PIC

CLICK for BIGGER PIC

6" / 5" Pocket Simplex Slide Rule
VERY LATE MODEL, BRAND NEW, Embossed white plastic construction, filled black scales. This is a great low cost pocket rule, admittedly generic in nature, probably from Japan in the 60's or 70's, but has no maker's marks at all. We get many requests for this kind of rule, always hard to keep in stock. Please note, these just come in a bag, and have no original instructions, we will provide a Pickett reprint that works with this rule. Just got one more batch, they will go FAST at this price! A great stocking stuffer! One rule CAN ship in a first class padded envelope for $6 if you feel brave. PLUS, we now have nice dark blue leatherette slip cases susan just made for these, add$5 each.

(6 Scales)
Front -
A, [ B, CI, C ] D, K

Still NEW bagged with reprint!

GREAT FEATURE! The CURSOR can't get lost, it's locked on the rule!

Have 140

Includes:
Reprint Sheet

$11 Ea. 6 Scale Rule Like this rule? CLICK TO ORDER 6 Scale Rule SLIDE RULE INFO / SCALES QUANTITY PRICE EACH ACUMATH Model No. 400 CLICK for BIGGER PIC CLICK for BIGGER PIC CLICK for BIGGER PIC 12" / 10" Simplex Mannheim Trig Slide Rule VERY LATE MODEL, NIB, BRAND NEW, complete in blister pack (two types) with brown/black vinyl slip case, and instruction sheet, and some are loose packed, mainly with brown/black cases (no blister pack). Embossed white plastic construction, black scales. A very useful and popular student rule, from the last production of the Sterling/Acumath/Borden Plastics amalgamation. We were incredibly lucky to find so many new factory packed sets still intact, they are great as a first student rule! Some have slightly different packaging, we will provide your choice if we can. (9 Scales) Front - S, K, A, [ B, CI, C ] D, L, T Still NEW factory packed! Have 5 Packed Have 7 Loose Includes: Blisterpack Sheet Case$35 Ea.

No. 400
Like this rule?

CLICK TO ORDER

SLIDE RULE
INFO / SCALES
QUANTITY
PRICE EA.

Aristo
Rietz-ST
912

CLICK for BIGGER PIC

12"/10" Scholar Slide Rule
NEW factory boxed sets, with 2 part plastic case, 100 Year Anniversary boxes, and even the inspection slip inside. The rule has a 4 line slightly magnifying cursor, plus two color (red/black) scale markings and scales are self-documenting on the right hand side. A very functional and attractive trig rule set, with a bonus top edge cm ruler. The back is blank, but the slide reverse has S, ST and T trig scales.. Includes box, 2-part case, and basic English reprint, because manuals were not included.

(10 Scales + cm Ruler)
Front - cm/ A, [ B, CI, C, ] D, L, K
Back - [ S, ST, T ]

Have 14

Includes:
BOX
Case
Manual Reprint

$49 Aristo 0912 Set Like this set? CLICK TO ORDER SLIDE RULE INFO / SCALES QUANTITY PRICE EACH PICKETT MICROLINE 120ES CLICK for BIGGER PIC FINALLY BACK IN STOCK! 12" / 10" Simplex Slide Rule VERY LATE MODEL, NIB, BRAND NEW, complete in factory box with leatherette case, and instruction sheet. Embossed yellow (eye-saver) plastic construction, black scales. A very useful student rule. We have had real trouble finding more ES/yellow sets, so don't miss these. This is the first stock in over a year, we got a whole factory case of new rules! (9 Scales) Front - K, A, [ B, S, T, CI, C ] D, L Still NEW factory packed! SORRY, SOLD Includes: Box Sheet Case$39 ea.

120ES
Like this rule?

CLICK TO ORDER

SLIDE RULE
INFO / SCALES
QUANTITY
PRICE EACH

PICKETT
MICROLINE
140(T)

CLICK for BIGGER PIC

CLICK for BIGGER PIC OF BACK

12" / 10" Log Log Trig Duplex Slide Rule - Excellent low cost advanced set!

VERY LATE MODEL, NIB, BRAND NEW, complete in factory box with leatherette case, "How to use Log Log Slide Rules" instruction manual. Engraved white plastic construction, black scales. This is a very sophisticated rule, made in a low cost format by Pickett, normally would have a T at the end for white Traditional, but just says 140, even though yellow ones say 140ES. Go figure. Nice new batch just arrived, quite a fluke to get so many at once.

(22 Scales)
Front - LL2-0.1, LL3-1.0, DF
[ CF, CIF, L, CI, C ]
D, LL2+0.1, LL3+1.0
Back - LL1-0.01, K, A,
[ B, Cos S, Sec T ST, T, C ]
D, DI, LL1+0.01

SORRY, SOLD
Includes:
Box
Manual
Case

$59 Ea. 140T Like this rule? CLICK TO ORDER SLIDE RULE INFO / SCALES QUANTITY PRICE EACH Aristo Junior 0901 12"/10" Junior Slide Rule NEW BOXED SETS complete with two part white and red plastic case. The rule has a 4 line slightly magnifying cursor, plus two color (red/black) scale markings with yellow accent coloring on the rule body stators. Self-documenting on the right hand side. A very functional and attractive basic rule set, with bonus folded scales. The back is blank. Includes 2-part case and english manual. Boxes may have some storage marks, contents are perfect. -RH (8 Scales) Front - DF, [ CF, CIF, CI, C, ] D, A, K Back - BLANK Last 2 Includes: Case Box Manual$49 Ea.

NEW Aristo 0901 Set
Like this set?

CLICK TO ORDER

SLIDE RULE
INFO / SCALES
QUANTITY
PRICE EA.

Aristo
Scholar
0903

CLICK for BIGGER PIC

12"/10" Scholar Slide Rule
USED, but Like NEW, classroom set of rules from germany that appears never to have been used. Some still have the inspection slip inside. Set has the two part white and red plastic case, all in excellent condition. The rule has a 4 line slightly magnifying cursor, plus two color (red/black) scale markings with yellow accent coloring on the rule body stators. Self-documenting on the right hand side. A very functional and attractive trig rule set, with a bonus BI scale, all with excellent documentation. The back is blank. Includes box, 2-part case, original manual (German) with some sets, plus we will include an expanded English reprint.

(11 Scales)
Front - L, K, A, [ B, BI, CI, C, ] D, S, ST, T
Back - BLANK

Last 1

Includes:

Case
Manual Reprint

$39 Aristo 0903 Set Like this set? CLICK TO ORDER SLIDE RULE INFO / SCALES QUANTITY PRICE EACH Blundell-Harling 904 Academy Duplex 10" Rule CLICK for BIGGER PIC CLICK for BIGGER PIC Great Deal - Almost GONE! 12.5" / 10" plastic body Slide Rule VERY LATE MODEL, VERY GOOD CONDITION. NEW, mint condition sets with blue/clear soft vinyl case and manual. Junior log log rule with a 2-color scale arrangement, it has 2 log-log scales, 3 trig scales plus folded scales. An attractive rule, with 3 line slightly magnifying plastic cursor (for area of a circle direct calculation), seldom seen in North America, made in England. (17 Scales, 3 Cursor lines) Front - ST, A, [ B, CI, C, ] D, S, T Back - K, L, DF, [ CF, CIF, C, ] D, LL2, L3 SORRY, SOLD Includes: Rule Soft Case Manual Save$6!
$49 Ea. Blundell 904 Like this rule? CLICK TO ORDER SLIDE RULE INFO / SCALES QUANTITY PRICE EACH PICKETT Basic Math 115 CLICK for BIGGER PIC 12" / 10" Simplex Slide Rule VERY EARLY MODEL, NIB, , complete in early factory box with leatherette case, and instruction booklet. Embossed white plastic construction, black scales. A very useful early math student rule, with remarkable scales, this can ADD and SUBTRACT (with positive and negative numbers!) and do Decade Counting! Extraordinary capability dropped from later Pickett rules, but invaluable to teach basic math with a slide rule. (8 Scales) Front - De, X, [ Y, CI, C ] D, A, L Still NEW factory packed! SORRY, SOLD Includes: Box Booklet Case$39 ea.

115
Like this rule?

CLICK TO ORDER

SLIDE RULE
INFO / SCALES
QUANTITY
PRICE EACH

PICKETT
MICROLINE 120T

CLICK for BIGGER PIC

12" / 10" Simplex Slide Rule
VERY LATE MODEL, NIB, BRAND NEW, complete in factory box with leatherette case, and instruction sheet. Embossed white plastic construction, black scales. A very useful student rule, and an ideal first slide rule gift! These are MINT condition, perfect. You can give this to very young kids, as it can be easily washed in a sink with a bit of dish detergent if it gets covered in PB+J. We have been out of these for a long time, glad to have some back!

(9 Scales)
Front -
K, A, [ B, S, T, CI, C ] D, L

Still NEW factory packed!

SORRY, SOLD

Includes:

Box
Sheet
Case

$36 ea. 120T Like this rule? CLICK TO ORDER SLIDE RULE INFO / SCALES QUANTITY PRICE EACH K & E 68-1892 K-12 Prep CLICK for bigger PIC! CLICK for bigger PIC! Includes: Slip Case Rule Manual K+E's upgraded format K-12 Student rule 12"/10" Full Size Slide Rule in updated body format K+E's stylish green and white student rule meant to look like a deci-lon. Engraved scales for ruggedness, and includes vinyl slip case and english factory manual. A very nice set for a new learner. Take all of them, and we will throw in the original retail display box! These are excellent condition, complete with everything, we pull all of them from the slip cases and clean any release agent off the rule (from the vinyl case). The back of the rule is blank. (9 Scales) Front - K, A, [ B, S, CI, T, C ] D, L CLICK for BIGGER PIC SORRY, SOLD Includes: Manual Slip Case$59 ea.

68-1892 (K12 Prep)
Like this rule?

CLICK TO ORDER

SLIDE RULE
INFO / SCALES
QUANTITY
PRICE EA.

Faber-Castell
Novo-Mentor
152/81

CLICK for BIGGER PIC

CLICK for OTHER SIDE

A great high end student rule from Faber-Castell!

12"/10" precision Slide Rule
BRAND NEW, MINT CONDITION! complete with 2-part ivory colored plastic case and factory manual in English!

Versatile duplex plastic body rule with 5 line cursor, pink color accent stripes on primary scales, and very useful mark-up/discount scale, and 5 dual purpose financial/math scales plus expanded trig scales. The rule is self documenting on right hand side for all scales. A very good quality rule with dual red/black scale markings. Excellent condition, and we get very few sets in this shape! (RH)

(17 Scales)
Front - A, DF, [ CF, CIF, CI, C, ] D , K
Back - L, T1, T2, [ S', CI, C, ] D, S, ST

SORRY, SOLD
Includes:
Case
English Manual

Now \$69

FC 152/81
Like this rule?

CLICK TO ORDER

 Other Places to go in the Slide Rule Universe:
 Click to visit! Buy a slide rule from our extensive on line marketplace, with restored classics, amazing new in the box rules, and low cost first student rules. We have something for everybody, even a swap and sell area for visitors. Click to visit! Learn to operate and care for your slide rule with these on line manuals and directions. Learn what scales mean, how to use them and how to restore or keep your rule in good condition. Click to visit! Tour our extensive archives of slide rule manufacturers and models from all over the world. Find out who made what, and what became of them after they stopped making slide rules. See how slide rules survive today in the form of slide charts still made in the millions annually. Click to visit! Visit other slide rule places on the web with more slide rule data and information. From personal collections on line to (yes, it's really true) the international slide rule owners and collectors organization, the Oughtred Society. Click to visit! Nice things people have said about us in print and on TV, see the original articles. We always appreciate it! Click to visit! Visit our TEST EQUIPMENT site everything from Scopes, CRT's and DMM's to nixie tubes, HP and Tektronix spare parts. A little electronic something for everybody. E-mail us You are visitor number 198204. Site Design & contents copyright 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2014, 2015, 2017, 2018 by Walter Shawlee 2 & the ad hoc Godzilla Graphics Group.