C₅×#71677 #14300688

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

Hall	C₃×C₅ ⋊ #1874
Sylow	C₃ ⋊ C₅×#1874

912 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 3 generators on 24 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 26386);