C₂×#13220 #495157

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

Aliases

1478 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 128

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

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

maximal subgroup of	#72312266, #72312274, C₂×#503195, …
maximal normal subgroup of	#72312266, #72312274, C₂×#503195, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402353);