Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C22 |
| direct product | C3×Q8×C24⋊C5 |
| unambiguous semidirect product | (C24×C3×Q8)⋊C5 |
| Fitting, Hall | C24×C3×Q8 ⋊ C5 |
| Sylow | C24×Q8 ⋊ C3×C5 |
1296 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 1296 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237216);