Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×#3584⋊C3 |
| unambiguous semidirect product | #3584⋊(C3×C5) |
| unambiguous semidirect product | (C5×#3584)⋊C3 |
| Fitting, Hall | C5×#3584 ⋊ C3 |
| Sylow | #3584 ⋊ C3×C5 |
668 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237075);