C₂×#8022 #181501

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

Aliases

2314 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88697);