C₂×#8234 #182759

order	512
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

1998 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 256

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

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

maximal subgroup of	#72279385, C₂×#210060, #72279458, …
maximal normal subgroup of	#72279385, C₂×#210060, #72279458, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 89955);