Finite Group DatabasebetaFinite Group Databasebeta| order | 9900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D99⋊D25 |
| unambiguous semidirect product | D225⋊D11 |
| unambiguous semidirect product | D275⋊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 ⋊ D9×D11 |
| 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 | D15⋊D11 |
| socle | C3×C5×C11 | D3×D5 |
| LCS | G ▷ C9×C11×C25 | |
| UCS | C1 | |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,11,3,5|c^3=f^2,d^5=g^4,c^a=c^2f,e^a=e^10,f^a=f^2,c^b=c^2f,d^b=d^4g,f^b=f^2,g^b=g^4654 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9900, 30);