C₂×#8642 #189050

order	512
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

1494 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 4 generators on 22 points:

(1,2);(3,4,5,6)(8,11)(9,13)(12,14)(15,16)(17,19)(18,21)(20,22);(7,8,9,11,10,12,13,14);(16,19)(17,22)(20,21)

maximal subgroup of	C₂×#211236, C₂×#225516, C₂×#220728
maximal normal subgroup of	C₂×#211236, C₂×#225516, C₂×#220728

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 96246);