C₅×#69485 #14304990

order	1920
isoclinism	isoclinic class of #4656
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₅ ⋊ #1940
Sylow	C₃ ⋊ C₅×#1940

496 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5)(6,7,8)(13,14,15,16)(17,20,21,22)(18,19,23,24);(7,8)(10,12)(17,19,22,23,21,24,20,18);(7,8)(9,10)(11,12)(14,16)(17,18,22,19,21,23,20,24)

420 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 30688);