C₂×#13010 #494484

order	512
nilpotency class	4
isoclinism	isoclinic class of #2238
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

1582 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)(7,8,12,15,22,19,10,20,11,16,21,18,13,9,17,14);(3,4,5,6)(7,9,13,8,11,19,22,16)(10,20,12,18,17,14,21,15);(10,17)(12,21)(14,20)(15,18)

maximal subgroup of	C₂×#511897, C₂×#512299, C₂×#495541
maximal normal subgroup of	C₂×#511897, C₂×#512299, C₂×#495541

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401680);