C₂×#8160 #182068

order	512
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁷

Aliases

1598 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

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

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

maximal subgroup of	#72313241, #72313254, #72313270, …
maximal normal subgroup of	#72313241, #72313254, #72313270, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89264);