C₂×#13219 #495147

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

Aliases

1810 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)(9,15,18,22)(10,19,16,14)(11,13)(12,17)(20,21);(7,9,16,17,11,18,10,20)(8,12,19,22,13,21,14,15);(3,4,5,6)(8,13)(12,21)(14,19)(15,22)

maximal subgroup of	C₂×#496333, C₂×#500781, #72312510, …
maximal normal subgroup of	C₂×#496333, C₂×#500781, #72312510, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402343);