Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C23×C4 |
| direct product | C5×#68952 |
| Fitting | C3×C5×#342 ⋊ C2 |
| Hall | C3×C5 ⋊ C4×#99 |
| Sylow | C3 ⋊ C4×C5×#99 |
824 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,3,4,5)(7,8)(9,11,12,10);(6,7,8)(13,15)(14,17,18,19)(16,20);(9,10,12,11)(13,14)(15,19)(16,18)(17,20)330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 21058);