Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×A4×Q32 |
| unambiguous semidirect product | (C22×Q32)⋊(C3×C5) |
| unambiguous semidirect product | (C22×C5×Q32)⋊C3 |
| Fitting, Hall | C22×C5×Q32 ⋊ C3 |
| Sylow | C22×Q32 ⋊ C3×C5 |
200 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236701);