Group cohomology of groups of order 32

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 prime-fifth order | group cohomology of groups of order 2^n

Group	Second part of GAP ID (GAP ID is (32,second part))	Hall-Senior number (among groups of order 32)	Hall-Senior symbol	Nilpotency class	Group cohomology page
Cyclic group:Z32	1	7	$(5)$	1	See group cohomology of finite cyclic groups
SmallGroup(32,2)	2	18	$\Gamma _{2}h$	2
Direct product of Z8 and Z4	3	5	$(32)$	1	See group cohomology of finite abelian groups
Semidirect product of Z8 and Z4 of M-type	4	19	$\Gamma _{2}i$	2
SmallGroup(32,5)	5	20	$\Gamma _{2}j_{1}$	2
Faithful semidirect product of E8 and Z4	6	46	$\Gamma _{7}a_{1}$	3
SmallGroup(32,7)	7	47	$\Gamma _{7}a_{2}$	3
SmallGroup(32,8)	8	48	$\Gamma _{7}a_{3}$	3
SmallGroup(32,9)	9	27	$\Gamma _{3}c_{1}$	3
SmallGroup(32,10)	10	28	$\Gamma _{3}c_{2}$	3
Wreath product of Z4 and Z2	11	31	$\Gamma _{3}e$	3
SmallGroup(32,12)	12	21	$\Gamma _{2}j_{2}$	2
Semidirect product of Z8 and Z4 of semidihedral type	13	30	$\Gamma _{3}d_{2}$	3
Semidirect product of Z8 and Z4 of dihedral type	14	29	$\Gamma _{3}d_{1}$	3
SmallGroup(32,15)	15	32	$\Gamma _{3}f$	3
Direct product of Z16 and Z2	16	6	$(41)$	1	See group cohomology of finite abelian groups
M32	17	22	$\Gamma _{2}k$	2
Dihedral group:D32	18	49	$\Gamma _{8}a_{1}$	4	See group cohomology of dihedral groups
Semidihedral group:SD32	19	50	$\Gamma _{8}a_{2}$	4	See group cohomology of semidihedral groups
Generalized quaternion group:Q32	20	51	$\Gamma _{8}a_{3}$	4	See group cohomology of dicyclic groups
Direct product of Z4 and Z4 and Z2	21	3	$(2^{2}1)$	1
Direct product of SmallGroup(16,3) and Z2	22	11	$\Gamma _{2}c_{1}$	2
Direct product of SmallGroup(16,4) and Z2	23	12	$\Gamma _{2}c_{2}$	2
SmallGroup(32,24)	24	16	$\Gamma _{2}f$	2
Direct product of D8 and Z4	25	14	$\Gamma _{2}e_{1}$	2
Direct product of Q8 and Z4	26	15	$\Gamma _{2}e_{2}$	2
SmallGroup(32,27)	27	33	$\Gamma _{4}a_{1}$	2
SmallGroup(32,28)	28	36	$\Gamma _{4}b_{1}$	2
SmallGroup(32,29)	29	37	$\Gamma _{4}b_{2}$	2
SmallGroup(32,30)	30	38	$\Gamma _{4}c_{1}$	2
SmallGroup(32,31)	31	39	$\Gamma _{4}c_{2}$	2
SmallGroup(32,32)	32	40	$\Gamma _{4}c_{3}$	2
SmallGroup(32,33)	33	41	$\Gamma _{4}d$	2
Generalized dihedral group for direct product of Z4 and Z4	34	34	$\Gamma _{4}a_{2}$	2	See group cohomology of generalized dihedral groups
SmallGroup(32,35)	35	35	$\Gamma _{4}a_{3}$	2
Direct product of Z8 and V4	36	4	$(31^{2})$	1	See group cohomology of finite abelian groups
Direct product of M16 and Z2	37	13	$\Gamma _{2}d$	2
Central product of D8 and Z8	38	17	$\Gamma _{2}g$	2
Direct product of D16 and Z2	39	23	$\Gamma _{3}a_{1}$	3
Direct product of SD16 and Z2	40	24	$\Gamma _{3}a_{2}$	3
Direct product of Q16 and Z2	41	25	$\Gamma _{3}a_{3}$	3
Central product of D16 and Z4	42	26	$\Gamma _{3}b$	3
Holomorph of Z8	43	44	$\Gamma _{6}a_{1}$	3
SmallGroup(32,44)	44	45	$\Gamma _{6}a_{2}$	3
Direct product of E8 and Z4	45	2	$(21^{3})$	1	See group cohomology of finite abelian groups
Direct product of D8 and V4	46	8	$\Gamma _{2}a_{1}$	2
Direct product of Q8 and V4	47	9	$\Gamma _{2}a_{2}$	2
Direct product of SmallGroup(16,13) and Z2	48	10	$\Gamma _{2}b$	2
Inner holomorph of D8	49	42	$\Gamma _{5}a_{1}$	2	See group cohomology of extraspecial groups
Central product of D8 and Q8	50	43	$\Gamma _{5}a_{2}$	2	See group cohomology of extraspecial groups
Elementary abelian group:E32	51	1	$(1^{5})$	1	See group cohomology of elementary abelian groups