C₂×#10843 #353631

order	512
nilpotency class	3
isoclinism	isoclinic class of #468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

3002 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 512

A minimal faithful permutation representation — 4 generators on 22 points:

(1,2);(3,4)(5,6)(8,10)(11,12,13,14)(16,20)(17,18)(21,22);(4,6)(15,16,18,22,19,21,17,20);(7,8,9,10)(16,21)(20,22)

maximal subgroup of	C₂×#414591, C₂×#360051, C₂×#360145, …
maximal normal subgroup of	C₂×#414591, C₂×#360051, C₂×#360145, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260827);