C₂×#10877 #353861

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

Aliases

2718 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)(7,8)(9,10)(15,16,19,17,18,20,22,21);(4,6)(11,12,13,14)(16,20)(17,21);(8,10)(15,17,19,20,18,21,22,16)

maximal subgroup of	C₂×#354295
maximal normal subgroup of	C₂×#354295

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261057);