C₂×#23190 #6382759

order	512
nilpotency class	3
isoclinism	isoclinic class of #3264
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

3290 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 5 generators on 18 points:

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

maximal subgroup of	C₂×D₄×#440, C₂×#6578595, C₂×#6578236
maximal normal subgroup of	C₂×D₄×#440, C₂×#6578595, C₂×#6578236

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6289955);