C₂×#13756 #513339

order	512
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄² · Schur multiplier (H₂) = C₂⁹×C₄²

Aliases

11634 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 420535);