C₂×#9397 #200488

order	512
nilpotency class	3
isoclinism	isoclinic class of #9383
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

2142 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);(4,7)(5,8)(9,10)(11,12,16,18,15,13,14,17);(3,4,8,10,6,9,5,7)(11,13,15,12)(14,17,16,18);(14,16)(17,18)

maximal subgroup of	C₂×#247880, C₂×#247879, C₂×#200521, …
maximal normal subgroup of	C₂×#247880, C₂×#247879, C₂×#200521, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 107684);