Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#68170 |
| Fitting | C3×C5×D4⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #1483 |
| Sylow | C3 ⋊ C5×#1483 |
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)(7,8)(10,14)(13,16);(6,7,8)(9,10)(11,16)(12,14)(13,15)(17,19)(18,21)(20,22)(23,24);(10,13)(11,15)(14,16)(17,18,20,23,21,19,24,22)330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 7613);