Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23×C4 |
| direct product | C5×#71586 |
| Fitting | C2×C3×C5×#117 ⋊ C2 |
| Hall | C3×C5 ⋊ #1875 |
| Sylow | C3 ⋊ C5×#1875 |
824 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)(14,16)(17,20,21,22)(18,23,19,24);(9,11,12,10)(17,19,21,18)(20,24,22,23);(7,8)(9,10,12,11)(13,14)(15,16)(17,18,22,23,21,19,20,24)390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 26428);