C₂×#13217 #495145

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

Aliases

1466 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)(9,15,18,22)(10,19,16,13)(11,14)(12,17)(20,21);(7,9,16,17,11,18,10,20)(8,12,19,22,14,21,13,15);(3,4,5,6)

maximal subgroup of	#72312266, #72312276, C₂×#500770, …
maximal normal subgroup of	#72312266, #72312276, C₂×#500770, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 402341);