C₂×#9221 #197696

order	512
nilpotency class	3
isoclinism	isoclinic class of #1665
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

1958 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)(15,16,17,21,19,22,18,20);(7,8,12,14,10,13,9,11)(16,20)(17,18)(21,22);(4,6)(16,21)(17,18)(20,22)

maximal subgroup of	C₂×#211236, C₂×#220728, C₂×#227078, …
maximal normal subgroup of	C₂×#211236, C₂×#220728, C₂×#227078, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 104892);