C₅×#83586 #14471903

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅ · Schur multiplier (H₂) = C₂⁴

Aliases

Hall	C₃×C₅ ⋊ #3362
Sylow	C₃ ⋊ C₅×#3362

784 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 960

A minimal faithful permutation representation — 4 generators on 24 points:

(1,2,3,4,5)(6,7,8)(9,11,12,16)(10,14,13,15);(7,8)(17,18,20,22)(19,24,23,21);(9,10,12,13)(11,15,16,14);(10,13)(14,15)(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, 197601);