Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26 |
| direct product | C5×#76613 |
| Fitting | C3×C5×#391 ⋊ C2 |
| Hall | C3×C5 ⋊ #2339 |
| Sylow | C3 ⋊ C5×#2339 |
1856 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3,4,5)(6,7)(18,21)(22,24);(7,8)(14,16)(17,19,20,23)(18,22,21,24);(7,8)(17,18)(19,22)(20,21)(23,24);(9,10,11,12)(13,14)(15,16)(18,21)(22,24)390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 51713);