C₅×#70363 #14299722

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

Aliases

Hall	C₃×C₅ ⋊ #1859
Sylow	C₃ ⋊ C₅×#1859

604 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 480

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 25420);