C₂×#9225 #197709

order	512
nilpotency class	3
isoclinism	isoclinic class of #1685
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

1634 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)(9,12)(13,14)(15,16,18,20,19,22,17,21);(7,8,12,14,10,13,9,11)(16,20)(17,18)(21,22);(4,6)(8,13)(11,14)(16,20)(17,18)(21,22)

maximal subgroup of	C₂×#249471, C₂×#249535, C₂×#197726, …
maximal normal subgroup of	C₂×#249471, C₂×#249535, C₂×#197726, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 104905);