C₃×#22476 #10641083

order	768
nilpotency class	3
isoclinism	isoclinic class of #17411
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

1696 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)(5,8)(9,11)(12,13)(14,18,19,16)(15,17);(4,5)(6,9)(7,8)(10,11);(4,6,7,10)(5,9,8,11)(12,14)(13,16)(15,19)(17,18);(5,8)(9,11)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 15464);