C₅×#82144 #14319669

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₅ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

Hall	C₃×C₅ ⋊ #2274
Sylow	C₃ ⋊ C₅×#2274

1392 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)(18,21)(22,24);(17,19,20,23)(18,22,21,24);(13,14,15,16)(18,21)(19,23);(7,8)(9,10,11,12)(17,18)(19,22)(20,21)(23,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45367);