C₂×#12791 #493683

order	512
nilpotency class	3
isoclinism	isoclinic class of #1812
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁶

Aliases

1354 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 64

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

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

maximal subgroup of	C₂×#494184, C₂×#511897, C₂×#512308
maximal normal subgroup of	C₂×#494184, C₂×#511897, C₂×#512308

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400879);