C₂×#13222 #495159

order	512
nilpotency class	4
isoclinism	isoclinic class of #11541
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

1822 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 22 points:

(1,2);(4,6)(7,8,11,14,10,13,18,20)(9,15,17,22,16,12,19,21);(7,9,11,19)(8,12,20,22)(10,16,18,17)(13,15,14,21);(3,4,5,6)(8,13)(12,15)(14,20)(21,22)

maximal subgroup of	C₂×#496333, C₂×#503468, C₂×#503206, …
maximal normal subgroup of	C₂×#496333, C₂×#503468, C₂×#503206, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402355);