C₂×#9832 #206095

order	512
nilpotency class	3
isoclinism	isoclinic class of #1714
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₈

Aliases

1938 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)(7,8)(9,13)(10,14)(11,12)(16,19)(17,20)(21,22);(4,6)(7,9,13,8,11,14,10,12);(8,12)(9,14)(15,16,20,22,18,21,17,19)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 113291);