Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C5×#68212 |
| Fitting | C3×C5×Q8⋊C8 ⋊ C2 |
| Hall | C3×C5 ⋊ C8×SD16 |
| Sylow | C3 ⋊ C5×C8×SD16 |
360 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)(9,11,12,16,13,10,14,15);(6,7,8)(17,18,20,22)(19,24,23,21);(9,10,12,15,13,11,14,16)(18,21)(19,23)(22,24)420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 11820);