C₅×#82094 #14322802

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₅ · Schur multiplier (H₂) = C₂⁵

Aliases

Hall	C₃×C₅ ⋊ #2315
Sylow	C₃ ⋊ C₅×#2315

1632 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)(18,22)(21,23);(13,14,15,16)(19,24)(21,23);(17,19)(18,21)(20,24)(22,23);(7,8)(9,10,11,12)(14,16)(17,18)(19,23)(20,22)(21,24)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 48500);