C₂×#11772 #481593

order	512
nilpotency class	4
isoclinism	isoclinic class of #11753
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

2562 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 18 points:

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

maximal subgroup of	C₂×#482357, C₂×#485933
maximal normal subgroup of	C₂×#482357, C₂×#485933

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 388789);