C₂×#8045 #181591

order	512
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

2146 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 4 generators on 22 points:

(1,2);(3,4,5,6)(8,12)(9,10)(13,14)(15,16)(17,21)(18,20)(19,22);(7,8,10,13,11,14,9,12)(16,20)(17,18)(21,22);(15,17,19,18)(16,21,22,20)

maximal subgroup of	C₂×#197777, C₂×#197729, C₂×#233936, …
maximal normal subgroup of	C₂×#197777, C₂×#197729, C₂×#233936, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88787);