Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#14559056 |
| unambiguous semidirect product | C3⋊(C3×#14559056) |
| derived | C3×C112 ⋊ C3×C4×C5 |
| Hall | C32×#10597244 ⋊ C4 |
| Hall | C3×C11×Dic33 ⋊ C5 |
| Hall | C32×C112 ⋊ C4×C5 |
| Hall | #10597244 ⋊ C3×Dic3 |
| Sylow | C112 ⋊ C3×C5×Dic3 |
| Sylow | C32 ⋊ #14559056 |
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
324 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 337);