Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#83688 |
| Fitting | C3×C5×#557 ⋊ C2 |
| Hall | C3×C5 ⋊ #3359 |
| Sylow | C3 ⋊ C5×#3359 |
740 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)(6,7,8)(9,11,12,16)(10,14,13,15);(7,8)(18,21)(19,24)(22,23);(9,10,12,13)(11,15,16,14);(10,13)(14,15)(17,18,20,23)(19,21,24,22)300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 197204);