C₅×#71708 #14282967

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂³

Aliases

Hall	C₃×C₅ ⋊ #1504
Sylow	C₃ ⋊ C₅×#1504

668 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 240

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 8665);