Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C25×C4 |
| direct product | C5×#71537 |
| Fitting | C22×C3×C42×C5 ⋊ C2 |
| Hall | C3×C5 ⋊ #1437 |
| Sylow | C3 ⋊ C5×#1437 |
1656 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)(6,7,8)(13,15,16,14)(22,24);(9,10,11,12)(18,20);(7,8)(13,14,16,15)(17,18)(19,20)(21,22,23,24)600 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 5705);