C₂×#12999 #494460

order	512
nilpotency class	4
isoclinism	isoclinic class of #2190
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

1622 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)(7,8,10,13,20,17,21,22,11,14,19,18,12,9,15,16);(3,4,5,6)(7,9)(8,12)(10,18)(11,17)(13,19)(14,20)(15,16)(21,22);(10,19)(13,18)(15,21)(16,22)

maximal subgroup of	C₂×#512308, C₂×#511881, C₂×#495541
maximal normal subgroup of	C₂×#512308, C₂×#511881, C₂×#495541

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 401656);