C₂×#14374 #520674

order	512
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁷×C₄²

Aliases

6254 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);(4,6)(11,12,13,14)(16,19)(17,21);(3,4,5,6)(8,10)(16,19)(20,22);(7,8)(9,10)(15,16,18,19)(17,20,21,22);(3,4)(5,6)(15,17)(16,20)(18,21)(19,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 427870);