C₅×#71674 #14283262

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

Aliases

Hall	C₃×C₅ ⋊ #1510
Sylow	C₃ ⋊ C₅×#1510

652 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 480

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 8960);