C₂×#11877 #482046

order	512
nilpotency class	4
isoclinism	isoclinic class of #11757
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

1872 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)(13,18)(16,17);(3,5,7,6)(4,8,10,9)(12,16)(13,18)

maximal subgroup of	C₂×#130768, #72282720, #72282727, …
maximal normal subgroup of	C₂×#130768, #72282720, #72282727, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 389242);