Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊((C11⋊C5)⋊D11) |
| unambiguous semidirect product | (C11⋊C5)⋊D99 |
| Fitting, derived, Hall | C9×C112 ⋊ C2×C5 |
| Hall | C9×C11×C11⋊C5 ⋊ C2 |
| Hall | C9⋊(C11⋊D11) ⋊ C5 |
| Hall | C11×C11⋊C5 ⋊ D9 |
| Sylow | C112 ⋊ C5×D9 |
| Sylow | C9 ⋊ (C11⋊C5)⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C112 | C2×C5 |
| Frattini | C3 | C3⋊((C11⋊C5)⋊D11) |
| socle | C3×C112 | C5×D3 |
| LCS | G ▷ C9×C112 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,3,11^2,3|c^3=f^2,c^a=c^2f,d^a=d^10,e^a=e^10,f^a=f^2,d^b=d^4354 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 55);