Group cohomology of groups of order 32

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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_2h 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_2i 2
SmallGroup(32,5) 5 20 \Gamma_2j_1 2
Faithful semidirect product of E8 and Z4 6 46 \Gamma_7a_1 3
SmallGroup(32,7) 7 47 \Gamma_7a_2 3
SmallGroup(32,8) 8 48 \Gamma_7a_3 3
SmallGroup(32,9) 9 27 \Gamma_3c_1 3
SmallGroup(32,10) 10 28 \Gamma_3c_2 3
Wreath product of Z4 and Z2 11 31 \Gamma_3e 3
SmallGroup(32,12) 12 21 \Gamma_2j_2 2
Semidirect product of Z8 and Z4 of semidihedral type 13 30 \Gamma_3d_2 3
Semidirect product of Z8 and Z4 of dihedral type 14 29 \Gamma_3d_1 3
SmallGroup(32,15) 15 32 \Gamma_3f 3
Direct product of Z16 and Z2 16 6 (41) 1 See group cohomology of finite abelian groups
M32 17 22 \Gamma_2k 2
Dihedral group:D32 18 49 \Gamma_8a_1 4 See group cohomology of dihedral groups
Semidihedral group:SD32 19 50 \Gamma_8a_2 4 See group cohomology of semidihedral groups
Generalized quaternion group:Q32 20 51 \Gamma_8a_3 4 See group cohomology of dicyclic groups
Direct product of Z4 and Z4 and Z2 21 3 (2^21) 1
Direct product of SmallGroup(16,3) and Z2 22 11 \Gamma_2c_1 2
Direct product of SmallGroup(16,4) and Z2 23 12 \Gamma_2c_2 2
SmallGroup(32,24) 24 16 \Gamma_2f 2
Direct product of D8 and Z4 25 14 \Gamma_2e_1 2
Direct product of Q8 and Z4 26 15 \Gamma_2e_2 2
SmallGroup(32,27) 27 33 \Gamma_4a_1 2
SmallGroup(32,28) 28 36 \Gamma_4b_1 2
SmallGroup(32,29) 29 37 \Gamma_4b_2 2
SmallGroup(32,30) 30 38 \Gamma_4c_1 2
SmallGroup(32,31) 31 39 \Gamma_4c_2 2
SmallGroup(32,32) 32 40 \Gamma_4c_3 2
SmallGroup(32,33) 33 41 \Gamma_4d 2
Generalized dihedral group for direct product of Z4 and Z4 34 34 \Gamma_4a_2 2 See group cohomology of generalized dihedral groups
SmallGroup(32,35) 35 35 \Gamma_4a_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_2d 2
Central product of D8 and Z8 38 17 \Gamma_2g 2
Direct product of D16 and Z2 39 23 \Gamma_3a_1 3
Direct product of SD16 and Z2 40 24 \Gamma_3a_2 3
Direct product of Q16 and Z2 41 25 \Gamma_3a_3 3
Central product of D16 and Z4 42 26 \Gamma_3b 3
Holomorph of Z8 43 44 \Gamma_6a_1 3
SmallGroup(32,44) 44 45 \Gamma_6a_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_2a_1 2
Direct product of Q8 and V4 47 9 \Gamma_2a_2 2
Direct product of SmallGroup(16,13) and Z2 48 10 \Gamma_2b 2
Inner holomorph of D8 49 42 \Gamma_5a_1 2 See group cohomology of extraspecial groups
Central product of D8 and Q8 50 43 \Gamma_5a_2 2 See group cohomology of extraspecial groups
Elementary abelian group:E32 51 1 (1^5) 1 See group cohomology of elementary abelian groups