Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#68343 |
| Fitting | C3×C5×#329 ⋊ C2 |
| Hall | C3×C5 ⋊ #1527 |
| Sylow | C3 ⋊ C5×#1527 |
528 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)(10,13)(14,16);(6,7,8)(10,13)(11,15)(17,18)(19,23)(20,22)(21,24);(9,10,11,14,12,13,15,16)(18,21,22,23)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 9729);