There are 51 groups of order 32 up to isomorphism. This page lists them.
The list
| Group |
GAP ID (second part) |
Abelian?
|
| Cyclic group:Z32 |
1 |
Yes
|
| SmallGroup(32,2) |
2 |
No
|
| Direct product of Z8 and Z4 |
3 |
Yes
|
| Semidirect product of Z8 and Z4 of M-type |
4 |
No
|
| SmallGroup(32,5) |
5 |
No
|
| Faithful semidirect product of E8 and Z4 |
6 |
No
|
| SmallGroup(32,7) |
7 |
No
|
| SmallGroup(32,8) |
8 |
No
|
| SmallGroup(32,9) |
9 |
No
|
| SmallGroup(32,10) |
10 |
No
|
| Wreath product of Z4 and Z2 |
11 |
No
|
| SmallGroup(32,12) |
12 |
No
|
| Semidirect product of Z8 and Z4 of semidihedral type |
13 |
No
|
| Semidirect product of Z8 and Z4 of dihedral type |
14 |
No
|
| SmallGroup(32,15) |
15 |
No
|
| Direct product of Z16 and Z2 |
16 |
Yes
|
| M32 |
17 |
No
|
| Dihedral group:D32 |
18 |
No
|
| Semidihedral group:SD32 |
19 |
No
|
| Generalized quaternion group:Q32 |
20 |
No
|
| Direct product of Z4 and Z4 and Z2 |
21 |
Yes
|
| Direct product of SmallGroup(16,3) and Z2 |
22 |
No
|
| Direct product of SmallGroup(16,4) and Z2 |
23 |
No
|
| SmallGroup(32,24) |
24 |
No
|
| Direct product of D8 and Z4 |
25 |
No
|
| Direct product of Q8 and Z4 |
26 |
No
|
| SmallGroup(32,27) |
27 |
No
|
| SmallGroup(32,28) |
28 |
No
|
| SmallGroup(32,29) |
29 |
No
|
| SmallGroup(32,30) |
30 |
No
|
| SmallGroup(32,31) |
31 |
No
|
| SmallGroup(32,32) |
32 |
No
|
| SmallGroup(32,33) |
33 |
No
|
| Generalized dihedral group for direct product of Z4 and Z4 |
34 |
No
|
| SmallGroup(32,35) |
35 |
No
|
| Direct product of Z8 and V4 |
36 |
Yes
|
| Direct product of M16 and Z2 |
37 |
No
|
| Central product of D8 and Z8 |
38 |
No
|
| Direct product of D16 and Z2 |
39 |
No
|
| Direct product of SD16 and Z2 |
40 |
No
|
| Direct product of Q16 and Z2 |
41 |
No
|
| Central product of D16 and Z4 |
42 |
No
|
| Holomorph of Z8 |
43 |
No
|
| SmallGroup(32,44) |
44 |
No
|
| Direct product of E8 and Z4 |
45 |
Yes
|
| Direct product of D8 and V4 |
46 |
No
|
| Direct product of Q8 and V4 |
47 |
No
|
| Direct product of SmallGroup(16,13) and Z2 |
48 |
No
|
| Inner holomorph of D8 |
49 |
No
|
| Central product of D8 and Q8 |
50 |
No
|
| Elementary abelian group:E32 |
51 |
Yes
|