C₅×#69777 #14307278

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

Aliases

Hall	C₃×C₅ ⋊ #1990
Sylow	C₃ ⋊ C₅×#1990

600 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)(13,15,16,20)(14,17,18,19);(9,11,12,10)(21,22,23,25,24,26,27,28);(7,8)(9,10,12,11)(13,14,16,18)(15,19,20,17)(22,25)(23,27)(26,28)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 32976);