Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#68361 |
| Fitting | C3×C5×#330 ⋊ C2 |
| Hall | C3×C5 ⋊ #1524 |
| Sylow | C3 ⋊ C5×#1524 |
468 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3,4,5)(6,7)(17,20,22,21)(18,23,19,24);(7,8)(9,10)(11,15)(12,14)(13,16)(17,19)(18,22)(20,24)(21,23);(10,13,14,15)(17,18,21,24,22,19,20,23)285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 9614);