C₅×#70186 #14304548

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²×C₄

Aliases

Hall	C₃×C₅ ⋊ #1934
Sylow	C₃ ⋊ C₅×#1934

584 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 30246);