C₂×#10835 #353615

order	512
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁸

Aliases

3042 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);(3,4)(5,6)(8,10)(11,12,13,14)(15,16,18,22,19,21,20,17);(4,6)(15,17,20,21,19,22,18,16);(7,8,9,10)(15,18,19,20)(16,17,21,22)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260811);