C₅×#69621 #14305172

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂×C₄

Aliases

Hall	C₃×C₅ ⋊ #1944
Sylow	C₃ ⋊ C₅×#1944

480 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)(7,8)(17,18,23,24,20,22,19,21);(6,7,8)(9,11,12,10)(14,16)(18,22)(21,24);(9,10,12,11)(13,14)(15,16)(18,21)(19,23)(22,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 30870);