C₂×#8963 #193794

order	512
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

2020 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);(3,4,7,9,6,5,8,10)(11,12,15,18,16,13,14,17);(3,5,7,10,6,4,8,9)(11,13,16,12)(14,17,15,18);(4,5)(9,10)(12,13)(14,15)

maximal subgroup of	C₂×#248071, C₂×#193833
maximal normal subgroup of	C₂×#248071, C₂×#193833

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 100990);