C₂×#8479 #187150

order	512
nilpotency class	3
isoclinism	isoclinic class of #8479
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

2924 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)(5,6,9,10)(7,8)(12,15,16,17);(3,5)(4,6)(7,9)(8,10)(11,12)(13,17)(14,16)(15,18);(3,6)(4,5)(7,10)(8,9)(13,18)(15,17)

maximal subgroup of	C₂×#187186
maximal normal subgroup of	C₂×#187186

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 94346);