Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#68120 |
| Fitting | C3×C5×#323 ⋊ C2 |
| Hall | C3×C5 ⋊ #1462 |
| Sylow | C3 ⋊ C5×#1462 |
880 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(7,8)(18,21)(22,24);(6,7,8)(9,11)(10,13)(12,16)(14,15);(9,10)(11,15,16,13)(12,14)(17,18,19,22,20,21,23,24)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 6650);