C₂×#11220 #358086

order	512
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁸

Aliases

2610 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)(8,9)(11,12,13,14)(15,16)(17,20)(18,19)(21,22);(7,8,10,9)(15,16,17,20)(18,19,22,21);(4,6)(7,9,10,8)(16,19)(18,22)(20,21)

maximal subgroup of	C₂×#394861, C₂×#358196, C₂×#395348, …
maximal normal subgroup of	C₂×#394861, C₂×#358196, C₂×#395348, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 265282);