Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#83864 |
| Fitting | C22×C3×C5×SD16 ⋊ C2 |
| Hall | C3×C5 ⋊ #3265 |
| Sylow | C3 ⋊ C5×#3265 |
1092 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,3,4,5)(6,7,8)(14,18)(15,20)(17,19);(10,12);(13,14,16,19)(15,18,20,17);(7,8)(9,10)(11,12)(14,17)(15,20)(18,19)285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 179146);