C₃×#7052 #10625659

order	768
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₈×C₁₆ · Schur multiplier (H₂) = C₈

Aliases

150 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 768

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,3)(4,5,6,10,7,11,12,17,8,9,13,15,14,16,18,19);(5,9)(10,15)(11,16)(17,19)(20,21,22,25,23,26,28,31,24,27,29,32,30,33,34,35)

maximal subgroup of	C₃×#122211, C₃×#123412, C₃×#123419, …
maximal normal subgroup of	C₃×#122211, C₃×#123412, C₃×#123419, …

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 40);