C₅×#82317 #14319717

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

Aliases

Hall	C₃×C₅ ⋊ #2275
Sylow	C₃ ⋊ C₅×#2275

1560 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)(18,22)(21,23);(13,15,16,14)(19,24)(21,23);(7,8)(9,10,11,12)(17,19)(18,21)(20,24)(22,23);(13,14,16,15)(17,18)(19,23)(20,22)(21,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 45415);