C₂×#11294 #358257

order	512
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

1762 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 64

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265453);