C₅×#68210 #14290642

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

Aliases

Hall	C₃×C₅ ⋊ #1651
Sylow	C₃ ⋊ C₅×#1651

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)(10,15)(11,12)(14,16);(7,8)(10,14)(11,12)(15,16)(17,18,20,22)(19,24,23,21);(7,8)(9,10,13,16)(11,14,12,15)(18,21)(19,23)(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, 16340);