Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25 |
| direct product | C5×#79773 |
| Fitting | C3×C5×#440 ⋊ C2 |
| Hall | C3×C5 ⋊ C4×AGL(1,ℤ/8) |
| Sylow | C3 ⋊ C4×C5×AGL(1,ℤ/8) |
1096 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)(14,18)(17,19);(7,8)(9,11,12,10);(14,17)(15,20)(18,19);(9,10,12,11)(13,14)(15,17)(16,18)(19,20)330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 142344);