Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C5×#68214 |
| Fitting | C3×C5×Q8⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ SD16⋊C8 |
| Sylow | C3 ⋊ C5×SD16⋊C8 |
352 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)(9,11,12,16,13,10,14,15)(18,22)(21,23);(7,8)(18,21)(19,24)(22,23);(7,8)(9,10,12,15,13,11,14,16)(17,18)(19,21)(20,22)(23,24)360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 11992);