C₅×#71746 #14283919

order	1920
isoclinism	isoclinic class of #4537
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₅ · Schur multiplier (H₂) = C₂²

Aliases

Hall	C₃×C₅ ⋊ #1524
Sylow	C₃ ⋊ C₅×#1524

468 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)(17,20,22,21)(18,23,19,24);(9,10)(11,15)(12,14)(13,16)(17,19)(18,22)(20,24)(21,23);(7,8)(10,13,14,15)(17,18,21,24,22,19,20,23)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 9617);