Finite Group DatabasebetaFinite Group Databasebeta| order | 9900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D25×D99 |
| unambiguous semidirect product | (C9×D25)⋊D11 |
| unambiguous semidirect product | (C11×D25)⋊D9 |
| Fitting, derived, Hall | C9×C11×C25 ⋊ C22 |
| Hall | C11×C25 ⋊ C2×D9 |
| Hall | C9×C25 ⋊ C2×D11 |
| Hall | C9×C11 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×D99 |
| Sylow | C11 ⋊ D9×D25 |
| Sylow | C9 ⋊ D11×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C11×C25 | C22 |
| Frattini | C3×C5 | D5×D33 |
| socle | C3×C5×C11 | D3×D5 |
| LCS | G ▷ C9×C11×C25 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
714 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9900, 28);