C₂×#8959 #193785

order	512
nilpotency class	3
isoclinism	isoclinic class of #453
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁷

Aliases

2108 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);(3,4,6,9,7,5,8,10)(11,12,16,18,15,13,14,17);(3,5,6,10,7,4,8,9)(11,13,15,12)(14,17,16,18);(14,16)(17,18)

maximal subgroup of	C₂×#247880, C₂×#247879, C₂×#193833, …
maximal normal subgroup of	C₂×#247880, C₂×#247879, C₂×#193833, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 100981);