Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C24 |
| direct product | C5×#68119 |
| Fitting | C3×C5×#323 ⋊ C2 |
| Hall | C3×C5 ⋊ #1459 |
| Sylow | C3 ⋊ C5×#1459 |
664 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(7,8)(9,11,13,12)(10,14,16,15);(6,7,8)(17,19)(18,21)(20,24)(22,23);(9,10,12,15,13,16,11,14)(17,18)(19,23,24,21)(20,22)330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 6541);