C₂×#21597 #6373116

order	512
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

2750 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)(9,14)(10,12)(11,13)(15,16,18,17,19,20,22,21);(7,9,11,10)(8,12,13,14);(4,6);(7,10,11,9)(8,12,13,14)(15,17,18,20,19,21,22,16)

maximal subgroup of	C₂×#6575930, C₂×#6578155, C₂×#6575914, …
maximal normal subgroup of	C₂×#6575930, C₂×#6578155, C₂×#6575914, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6280312);