C₂×#21060 #6371636

order	512
nilpotency class	3
isoclinism	isoclinic class of #3003
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

4390 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 5 generators on 18 points:

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

maximal subgroup of	#72315761, #72315970, C₂×#6381410
maximal normal subgroup of	#72315761, #72315970, C₂×#6381410

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6278832);