C₅×#69419 #14280241

order	1920
isoclinism	isoclinic class of #4656
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

Hall	C₃×C₅ ⋊ #1444
Sylow	C₃ ⋊ C₅×#1444

1216 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)(18,20)(21,22,23,24);(13,14,15,16)(17,18)(19,20);(7,8)(9,10,11,12)(14,16)(22,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 5939);