Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C11 |
| direct product | D9×C5⋊(C11⋊D11) |
| unambiguous semidirect product | (C5×D9)⋊(C11⋊D11) |
| unambiguous semidirect product | (C11×D9)⋊D55 |
| Fitting, derived, Hall | C5×C9×C112 ⋊ C22 |
| Hall | C9×C112 ⋊ C2×D5 |
| Hall | C5×C112 ⋊ C2×D9 |
| Sylow | C112 ⋊ D5×D9 |
| Hall | C5×C9 ⋊ C2×C11⋊D11 |
| Sylow | C9 ⋊ C2×C5⋊(C11⋊D11) |
| Sylow | C5 ⋊ D9×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C9×C112 | C22 |
| Frattini | C3 | D3×C5⋊(C11⋊D11) |
| socle | C3×C5×C112 | C2×D3 |
| LCS | G ▷ C5×C9×C112 | |
| UCS | C1 | |
420 conjugacy classes of subgroups.
1824 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 293);