C₂×#8567 #188360

order	512
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

1538 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)(9,11)(10,13)(12,14)(15,16,20,21,19,18,17,22);(3,4,5,6)(15,17,19,20)(16,21,18,22);(8,11)(9,14)(12,13)(15,18)(16,19)(17,21)(20,22)

maximal subgroup of	C₂×#225908, C₂×#210578, C₂×#225462, …
maximal normal subgroup of	C₂×#225908, C₂×#210578, C₂×#225462, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 95556);