C₅×#71763 #14301531

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

Hall	C₃×C₅ ⋊ #1887
Sylow	C₃ ⋊ C₅×#1887

888 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 20 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 27229);