C₂×#9365 #200023

order	512
nilpotency class	3
isoclinism	isoclinic class of #9345
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

2466 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 64

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

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

maximal subgroup of	#72231590, C₂×#200068
maximal normal subgroup of	#72231590, C₂×#200068

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 107219);