C₅×#71545 #14280004

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₅ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

Hall	C₃×C₅ ⋊ #1437
Sylow	C₃ ⋊ C₅×#1437

1656 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)(13,15,16,14)(22,24);(7,8)(9,10,11,12)(18,20);(13,14,16,15)(17,18)(19,20)(21,22,23,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 5702);