C₂×#9503 #201726

order	512
nilpotency class	3
isoclinism	isoclinic class of #9495
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

2840 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);(3,4,6,9,7,8,10,5)(11,12)(13,17,18,15)(14,16);(3,5,6,8,7,9,10,4)(11,12)(13,15)(14,16)(17,18);(11,13)(12,15)(14,18)(16,17)

maximal subgroup of	C₂×#201743
maximal normal subgroup of	C₂×#201743

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 108922);