Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C23×C4 |
| direct product | C5×#68780 |
| Fitting | C3×C5×#340 ⋊ C2 |
| Hall | C3×C5 ⋊ C4×#102 |
| Sylow | C3 ⋊ C4×C5×#102 |
792 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)(13,15,16,14);(6,7,8)(9,10,11,12)(17,18,20,23,21,24,19,22);(13,14,16,15)(18,22)(19,20)(23,24)420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 21384);