C₂×#8945 #193532

order	512
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁷

Aliases

1764 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);(4,6)(7,8,10,12,11,14,9,13)(15,16,18,21,19,17,20,22);(3,4,5,6)(8,12)(9,10)(13,14)(15,17,18,22,19,16,20,21);(8,12)(9,10)(13,14)

maximal subgroup of	C₂×#249463, C₂×#244792, C₂×#193537, …
maximal normal subgroup of	C₂×#249463, C₂×#244792, C₂×#193537, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 100728);