C₃×#21778 #10640385

order	768
nilpotency class	3
isoclinism	isoclinic class of #21776
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

1440 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 4 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 14766);