Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#68236 |
| Fitting | C3×C5×Q8⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ #1487 |
| Sylow | C3 ⋊ C5×#1487 |
496 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)(10,13)(14,16);(6,7,8)(17,18,20,22)(19,24,23,21);(9,10,11,14,12,13,15,16)(18,21)(19,23)(22,24)330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 7805);