Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26 |
| direct product | C5×#73577 |
| Fitting | C3×C4×C5×C22⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #2358 |
| Sylow | C3 ⋊ C5×#2358 |
1856 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)(18,20);(7,8)(14,16);(9,11,12,10)(17,18)(19,20);(7,8)(9,10,12,11)(13,14)(15,16)(18,20)450 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 53808);