Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×D9×#10597244 |
| unambiguous semidirect product | C9⋊(C22×#10597244) |
| unambiguous semidirect product | (C2×C9)⋊(C2×#10597244) |
| Fitting | C2×C9×C112 ⋊ C2×C5 |
| derived, Hall | C9×C112 ⋊ C22×C5 |
| Hall | C9×#10597244 ⋊ C22 |
| Hall | C2×C112×D9 ⋊ C5 |
| Sylow | C112 ⋊ C2×C5×D9 |
| Sylow | C9 ⋊ C22×#10597244 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D9×#10597244 |
| commutator, cosocle, hypocenter | C9×C112 | C22×C5 |
| Frattini | C3 | C2×D3×#10597244 |
| Fitting | C2×C9×C112 | C2×C5 |
| socle | C2×C3×C112 | C5×D3 |
| LCS | G ▷ C9×C112 | |
| UCS | C1 ◁ C2 | |
150 conjugacy classes of subgroups.
348 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 251);