C₅×#68605 #14298705

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅×C₈ · Schur multiplier (H₂) = C₂²×C₄

Aliases

Hall	C₃×C₅ ⋊ #1831
Sylow	C₃ ⋊ C₅×#1831

520 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 1920

A minimal faithful permutation representation — 3 generators on 28 points:

(1,2,3,4,5)(6,7,8)(9,11,12,10)(22,26)(25,28);(7,8)(9,10,12,11)(21,23,24,27)(22,25,26,28);(10,11)(13,14,15,17,16,18,19,20)(21,22)(23,25)(24,26)(27,28)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 24403);