C₃×#21793 #10640400

order	768
nilpotency class	3
isoclinism	isoclinic class of #17392
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₄ · Schur multiplier (H₂) = C₂⁴×C₄²

Aliases

1882 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 96

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 14781);