C₅×#69731 #14285681

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

Aliases

Hall	C₃×C₅ ⋊ #1567
Sylow	C₃ ⋊ C₅×#1567

368 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)(6,7,8)(10,13)(14,16);(17,18,22,24,20,23,19,21);(7,8)(9,10,11,14,12,13,15,16)(18,21)(19,22)(23,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 11379);