Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22×C4 |
| direct product | C5×#68278 |
| Fitting | C3×C5×#327 ⋊ C2 |
| Hall | C3×C5 ⋊ #1505 |
| Sylow | C3 ⋊ C5×#1505 |
544 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)(10,15,16,14);(6,7,8)(10,14)(11,12)(15,16)(17,18)(19,23)(20,22)(21,24);(9,10)(11,15)(12,14)(13,16)(18,21,22,23)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 8719);