C₂×#8177 #182153

order	512
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

1674 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);(3,4,6,5)(7,8,10,13)(9,11,14,12)(16,20)(17,18)(21,22);(8,11,13,12)(15,16,18,21,19,22,17,20);(3,5,6,4)(15,17,19,18)(16,20,22,21)

maximal subgroup of	C₂×#184300, C₂×#229758, C₂×#183891, …
maximal normal subgroup of	C₂×#184300, C₂×#229758, C₂×#183891, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89349);