C₂×#22750 #6380443

order	512
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

2982 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)(9,12)(10,14)(11,13)(15,16,18,20,17,19,21,22);(3,4)(5,6)(7,9,11,10)(8,12,13,14)(16,19)(20,22);(7,10,11,9)(8,12,13,14);(4,6)

maximal subgroup of	C₂×#6576050, C₂×#6575400, C₂×D₄×#432, …
maximal normal subgroup of	C₂×#6576050, C₂×#6575400, C₂×D₄×#432, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6287639);