Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C5⋊#994 |
| unambiguous semidirect product | (C4×#4149)⋊C3 |
| Hall | C4×#4149 ⋊ C3 |
| Sylow | C5 ⋊ C4×#994 |
760 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
188 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 239721);