Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C9×#11925894⋊C2 |
| unambiguous semidirect product | #11925894⋊(C2×C9) |
| unambiguous semidirect product | #11925897⋊(C2×C9) |
| unambiguous semidirect product | #11925898⋊(C2×C9) |
| Fitting, Hall | C9×C112 ⋊ C22×C5 |
| derived, Sylow | C112 ⋊ C22×C5×C9 |
| Hall | C9×#10597244 ⋊ C22 |
| Hall | C9×D112 ⋊ C5 |
| Hall | #10597244 ⋊ C22×C9 |
| Hall | D112 ⋊ C5×C9 |
126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
261 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 178);