C₂×#9785 #205744

order	512
nilpotency class	3
isoclinism	isoclinic class of #9784
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

1630 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 128

A minimal faithful permutation representation — 4 generators on 18 points:

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

maximal subgroup of	#72313306, #72313311, C₂×#220244, …
maximal normal subgroup of	#72313306, #72313311, C₂×#220244, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 112940);