C₅×#69484 #14304931

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₈ · Schur multiplier (H₂) = C₂³

Aliases

Hall	C₃×C₅ ⋊ #1939
Sylow	C₃ ⋊ C₅×#1939

520 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);(7,8)(10,12)(17,19,20,24,21,18,22,23);(7,8)(9,10)(11,12)(14,16)(17,18,20,23,21,19,22,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 30629);