Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#3416⋊C3 |
| unambiguous semidirect product | #3416⋊(C3×C5) |
| unambiguous semidirect product | (C5×#3416)⋊C3 |
| Fitting, Hall | C5×#3416 ⋊ C3 |
| Sylow | #3416 ⋊ C3×C5 |
200 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236703);