This article gives specific information, namely, group cohomology, about a family of groups, namely: groups of order 32.
View group cohomology of group families  View group cohomology of groups of a particular order View other specific information about groups of order 32
This page describes the theory behind the homology and cohomology groups of groups of order 32.
View these in a broader context: group cohomology of groups of primefifth order  group cohomology of groups of order 2^n
Group 
Second part of GAP ID (GAP ID is (32,second part)) 
HallSenior number (among groups of order 32) 
HallSenior symbol 
Nilpotency class 
Group cohomology page

Cyclic group:Z32 
1 
7 

1 
See group cohomology of finite cyclic groups

SmallGroup(32,2) 
2 
18 

2 

Direct product of Z8 and Z4 
3 
5 

1 
See group cohomology of finite abelian groups

Semidirect product of Z8 and Z4 of Mtype 
4 
19 

2 

SmallGroup(32,5) 
5 
20 

2 

Faithful semidirect product of E8 and Z4 
6 
46 

3 

SmallGroup(32,7) 
7 
47 

3 

SmallGroup(32,8) 
8 
48 

3 

SmallGroup(32,9) 
9 
27 

3 

SmallGroup(32,10) 
10 
28 

3 

Wreath product of Z4 and Z2 
11 
31 

3 

SmallGroup(32,12) 
12 
21 

2 

Semidirect product of Z8 and Z4 of semidihedral type 
13 
30 

3 

Semidirect product of Z8 and Z4 of dihedral type 
14 
29 

3 

SmallGroup(32,15) 
15 
32 

3 

Direct product of Z16 and Z2 
16 
6 

1 
See group cohomology of finite abelian groups

M32 
17 
22 

2 

Dihedral group:D32 
18 
49 

4 
See group cohomology of dihedral groups

Semidihedral group:SD32 
19 
50 

4 
See group cohomology of semidihedral groups

Generalized quaternion group:Q32 
20 
51 

4 
See group cohomology of dicyclic groups

Direct product of Z4 and Z4 and Z2 
21 
3 

1 

Direct product of SmallGroup(16,3) and Z2 
22 
11 

2 

Direct product of SmallGroup(16,4) and Z2 
23 
12 

2 

SmallGroup(32,24) 
24 
16 

2 

Direct product of D8 and Z4 
25 
14 

2 

Direct product of Q8 and Z4 
26 
15 

2 

SmallGroup(32,27) 
27 
33 

2 

SmallGroup(32,28) 
28 
36 

2 

SmallGroup(32,29) 
29 
37 

2 

SmallGroup(32,30) 
30 
38 

2 

SmallGroup(32,31) 
31 
39 

2 

SmallGroup(32,32) 
32 
40 

2 

SmallGroup(32,33) 
33 
41 

2 

Generalized dihedral group for direct product of Z4 and Z4 
34 
34 

2 
See group cohomology of generalized dihedral groups

SmallGroup(32,35) 
35 
35 

2 

Direct product of Z8 and V4 
36 
4 

1 
See group cohomology of finite abelian groups

Direct product of M16 and Z2 
37 
13 

2 

Central product of D8 and Z8 
38 
17 

2 

Direct product of D16 and Z2 
39 
23 

3 

Direct product of SD16 and Z2 
40 
24 

3 

Direct product of Q16 and Z2 
41 
25 

3 

Central product of D16 and Z4 
42 
26 

3 

Holomorph of Z8 
43 
44 

3 

SmallGroup(32,44) 
44 
45 

3 

Direct product of E8 and Z4 
45 
2 

1 
See group cohomology of finite abelian groups

Direct product of D8 and V4 
46 
8 

2 

Direct product of Q8 and V4 
47 
9 

2 

Direct product of SmallGroup(16,13) and Z2 
48 
10 

2 

Inner holomorph of D8 
49 
42 

2 
See group cohomology of extraspecial groups

Central product of D8 and Q8 
50 
43 

2 
See group cohomology of extraspecial groups

Elementary abelian group:E32 
51 
1 

1 
See group cohomology of elementary abelian groups
