Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×D11×D45 |
| unambiguous semidirect product | (C5×D11)⋊(C11×D9) |
| unambiguous semidirect product | (C9×D11)⋊(D5×C11) |
| Fitting, Hall | C5×C9×C112 ⋊ C22 |
| derived | C5×C9×C11 ⋊ C22×C11 |
| Hall | C9×C112 ⋊ C2×D5 |
| Hall | C5×C112 ⋊ C2×D9 |
| Sylow | C112 ⋊ C2×D45 |
| Hall | C5×C9 ⋊ C2×C11×D11 |
| Sylow | C9 ⋊ D5×C11×D11 |
| Sylow | C5 ⋊ C11×D9×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D11×D45 |
| commutator, cosocle, hypocenter | C5×C9×C11 | C22×C11 |
| Frattini | C3 | C11×D11×D15 |
| Fitting | C5×C9×C112 | C22 |
| socle | C3×C5×C112 | C2×D3 |
| LCS | G ▷ C5×C9×C11 | |
| UCS | C1 ◁ C11 | |
180 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1848 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 283);