Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of #120⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C4×C5×#120⋊C3 |
| unambiguous semidirect product | (C4×#120)⋊(C3×C5) |
| unambiguous semidirect product | (C4×C5×#120)⋊C3 |
| Fitting, Hall | C4×C5×#120 ⋊ C3 |
| derived | C24 ⋊ C2×C3×C4×C5 |
| Sylow | C4×#120 ⋊ C3×C5 |
508 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236593);