Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×#80049 |
| Fitting | C3×C5×#448 ⋊ C2 |
| Hall | C3×C5 ⋊ #3298 |
| Sylow | C3 ⋊ C5×#3298 |
840 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 960 |
A minimal faithful permutation representation — 4 generators on 24 points:
(1,2,3,4,5)(6,7,8)(11,16)(13,15);(17,18,20,22)(19,24,23,21);(7,8)(9,11)(10,13)(12,16)(14,15);(7,8)(9,10,12,14)(11,15,16,13)(18,21)(19,23)(22,24)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 184798);