Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of C24⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C4×C24⋊C5 |
| unambiguous semidirect product | (C25×C3×C4)⋊C5 |
| Fitting, Hall | C25×C3×C4 ⋊ C5 |
| derived | C24 ⋊ C2×C3×C4×C5 |
| Sylow | C25×C4 ⋊ C3×C5 |
2168 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 2168 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) = 120 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237214);