C₂×#21955 #6374893

order	512
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

2714 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)(7,8)(9,13)(10,12)(11,14)(15,16,19,20,18,21,17,22);(7,9,10,14)(8,11,12,13)(15,17,18,19)(16,20,21,22);(3,4,5,6)(9,14)(11,13);(8,12)(11,13)

maximal subgroup of	C₂×#6481762, C₂×#6519691, C₂×#6388672
maximal normal subgroup of	C₂×#6481762, C₂×#6519691, C₂×#6388672

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6282089);