C₂×#7556 #153733

order	512
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂¹¹

Aliases

9506 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 512

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 60929);