C₅×#69643 #14308908

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

Aliases

Hall	C₃×C₅ ⋊ #2027
Sylow	C₃ ⋊ C₅×#2027

564 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 480

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 34606);