C₅×#83483 #14458452

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

Aliases

Hall	C₃×C₅ ⋊ #3295
Sylow	C₃ ⋊ C₅×#3295

924 conjugacy classes of subgroups.

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

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 184150);