C₅×#68904 #14297675

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

Aliases

Hall	C₃×C₅ ⋊ #1803
Sylow	C₃ ⋊ C₅×#1803

616 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)(6,7)(17,18,20,22)(19,24,23,21);(7,8)(13,14,15,16);(9,10,11,12)(14,16)(18,21)(19,23)(22,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 23373);