Category:Particular groups
This is a category of articles about particular objects or specific concrete examples in a certain collection of objects
This page lists particular groups, viz groups, each unique up to isomorphism.
See also number of groups of given order to get an idea of how many groups there are of particular orders, along with links to pages that compare and contrast groups of a particular order.
If you want to search for a group given its group ID as per the SmallGroup library for GAP or Magma, type in SmallGroup(order,ID) into the search bar at the top right of the page. For instance, if the ID is (32,33), type in SmallGroup(32,33) in the search bar. If the ID is (12,3), type in SmallGroup(12,3) in the search bar.
Particular groups of importance
Extremely important (importance rank 1):
| GAP ID | |
|---|---|
| Cyclic group:Z2 | 2 (1) |
| Cyclic group:Z3 | 3 (1) |
| Symmetric group:S3 | 6 (1) |
Very important (importance rank 2):
| GAP ID | |
|---|---|
| Alternating group:A4 | 12 (3) |
| Alternating group:A6 | 360 (118) |
| Dihedral group:D8 | 8 (3) |
| Projective special linear group:PSL(3,2) | 168 (42) |
| Quaternion group | 8 (4) |
| Symmetric group:S4 | 24 (12) |
Somewhat important (importance rank 3):
Pages in category "Particular groups"
The following 200 pages are in this category, out of 643 total. The count includes redirect pages that have been included in the category. Redirect pages are shown in italics.
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- Direct product of D8 and V4
- Direct product of D8 and Z2
- Direct product of D8 and Z3
- Direct product of D8 and Z4
- Direct product of D8 and Z4 and Z2
- Direct product of D8 and Z5
- Direct product of D8 and Z6
- Direct product of D8 and Z7
- Direct product of Dic12 and Z2
- Direct product of E16 and Z4
- Direct product of E4 and E9
- Direct product of E4 and Z9
- Direct product of E8 and Q8
- Direct product of E8 and Z3
- Direct product of E8 and Z4
- Direct product of E9 and Z4
- Direct product of group of rational numbers and group of rational numbers modulo integers
- Direct product of holomorph of Z8 and Z2
- Direct product of M16 and V4
- Direct product of M16 and Z2
- Direct product of M16 and Z3
- Direct product of M16 and Z4
- Direct product of M27 and Z3
- Direct product of M32 and Z2
- Direct product of prime-cube order group:U(3,3) and Z3
- Direct product of Q16 and V4
- Direct product of Q16 and Z2
- Direct product of Q16 and Z3
- Direct product of Q16 and Z4
- Direct product of Q32 and Z2
- Direct product of Q8 and Q8
- Direct product of Q8 and S3
- Direct product of Q8 and V4
- Direct product of Q8 and Z2
- Direct product of Q8 and Z3
- Direct product of Q8 and Z4
- Direct product of Q8 and Z5
- Direct product of S3 and D10
- Direct product of S3 and GL(2,3)
- Direct product of S3 and S3
- Direct product of S3 and S4
- Direct product of S3 and Z3
- Direct product of S3 and Z4
- Direct product of S3 and Z7
- Direct product of S4 and V4
- Direct product of S4 and Z2
- Direct product of S4 and Z3
- Direct product of S4 and Z4
- Direct product of S4 and Z5
- Direct product of S5 and V4
- Direct product of S5 and Z2
- Direct product of SD16 and V4
- Direct product of SD16 and Z2
- Direct product of SD16 and Z3
- Direct product of SD16 and Z4
- Direct product of SD32 and Z2
- Direct product of SL(2,3) and V4
- Direct product of SL(2,3) and Z2
- Direct product of SL(2,3) and Z3
- Direct product of SL(2,3) and Z4
- Direct product of SL(2,5) and PSL(3,2)
- Direct product of SL(2,5) and SL(2,7)
- Direct product of SL(2,5) and Z2
- Direct product of SmallGroup(16,13) and V4
- Direct product of SmallGroup(16,13) and Z2
- Direct product of SmallGroup(16,13) and Z4
- Direct product of SmallGroup(16,3) and V4
- Direct product of SmallGroup(16,3) and Z3
- Direct product of SmallGroup(16,3) and Z4
- Direct product of SmallGroup(16,4) and V4
- Direct product of SmallGroup(16,4) and Z4
- Direct product of SmallGroup(32,12) and Z2
- Direct product of SmallGroup(32,13) and Z2
- Direct product of SmallGroup(32,14) and Z2
- Direct product of SmallGroup(32,2) and Z2
- Direct product of SmallGroup(32,24) and Z2
- Direct product of SmallGroup(32,27) and Z2
- Direct product of SmallGroup(32,33) and Z2
- Direct product of SmallGroup(32,4) and Z2
- Direct product of SmallGroup(32,49) and Z2
- Direct product of SmallGroup(32,50) and Z2
- Direct product of V4 and D14
- Direct product of V4 and Z14
- Direct product of Z and Z2
- Direct product of Z10 and S3
- Direct product of Z10 and Z2
- Direct product of Z16 and V4
- Direct product of Z16 and Z2
- Direct product of Z16 and Z4
- Direct product of Z2 and Dic28
- Direct product of Z2 and GA(2,3)
- Direct product of Z2 and GL(2,3)
- Direct product of Z2 and semidirect product of Z11 and Z5
- Direct product of Z2 and SmallGroup(54,6)
- Direct product of Z2 and the semidirect product of Z7 and Z3
- Direct product of Z2 and Z14
- Direct product of Z2 and Z28
- Direct product of Z2 and Z30
- Direct product of Z27 and E9
- Direct product of Z27 and Z3
- Direct product of Z27 and Z9
- Direct product of Z3 and D10
- Direct product of Z3 and Dic20
- Direct product of Z3 and GA(1,5)
- Direct product of Z3 and SmallGroup(40,1)
- Direct product of Z3 and SmallGroup(40,3)
- Direct product of Z3 and SmallGroup(40,8)
- Direct product of Z3 and the Frobenius group of order 21
- Direct product of Z32 and Z2
- Direct product of Z4 and D14
- Direct product of Z4 and V4
- Direct product of Z4 and Z2
- Direct product of Z4 and Z4
- Direct product of Z4 and Z4 and V4
- Direct product of Z4 and Z4 and Z2
- Direct product of Z4 and Z4 and Z4
- Direct product of Z5 and A4
- Direct product of Z5 and Dic12
- Direct product of Z5 and GA(1,5)
- Direct product of Z5 and S3
- Direct product of Z5 and SL(2,3)
- Direct product of Z5 and SmallGroup(24,1)
- Direct product of Z6 and D10
- Direct product of Z6 and Z2
- Direct product of Z6 and Z3
- Direct product of Z6 and Z4
- Direct product of Z7 and D8
- Direct product of Z7 and Q8
- Direct product of Z8 and D8
- Direct product of Z8 and E8
- Direct product of Z8 and V4
- Direct product of Z8 and Z2
- Direct product of Z8 and Z4
- Direct product of Z8 and Z4 and V4
- Direct product of Z8 and Z4 and Z2
- Direct product of Z8 and Z8
- Direct product of Z81 and Z3
- Direct product of Z9 and E27
- Direct product of Z9 and E9
- Direct product of Z9 and Z3
- Direct product of Z9 and Z9
- Direct product of Z9 and Z9 and Z3
- Double cover of alternating group:A7
- Double cover of alternating group:A8
- Double cover of projective special linear group:PSL(3,4)
- Double cover of symmetric group:S5 of minus type
- Double cover of symmetric group:S5 of plus type
E
F
- Finitary alternating group of countable degree
- Finitary alternating group on the natural numbers
- Finitary symmetric group of countable degree
- Fischer group:Fi22
- Fischer group:Fi23
- Free abelian group of countable rank
- Free abelian group of rank three
- Free abelian group of rank two
- Free group of countable rank
- Free group:F2
- Free group:F3
- Free product of class two of two Klein four-groups
- Fundamental group of Klein bottle
G
- GAPlus(1,R)
- General affine group:GA(1,11)
- General affine group:GA(1,5)
- General affine group:GA(1,7)
- General affine group:GA(1,8)
- General affine group:GA(1,9)
- General affine group:GA(1,Q)
- General affine group:GA(2,3)
- General linear group:GL(2,11)
- General linear group:GL(2,13)
- General linear group:GL(2,3)
- General linear group:GL(2,4)
- General linear group:GL(2,5)
- General linear group:GL(2,7)
- General linear group:GL(2,8)
- General linear group:GL(2,9)
- General linear group:GL(2,H)
- General linear group:GL(2,Q)
- General linear group:GL(2,Z)
- General linear group:GL(2,Z4)
- General linear group:GL(2,Z9)
- General linear group:GL(3,3)
- General semiaffine group:GammaA(1,9)
- General semilinear group:GammaL(1,8)
- Generalized dihedral group for 2-quasicyclic group
- Generalized dihedral group for additive group of 2-adic integers
- Generalized dihedral group for direct product of Z4 and Z4
- Generalized dihedral group for E9
- Generalized quaternion group:Q1024
- Generalized quaternion group:Q128