Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C11 |
| direct product | C5×C9⋊(C11⋊D11) |
| unambiguous semidirect product | C9⋊(C5×C11⋊D11) |
| Fitting, Hall | C5×C9×C112 ⋊ C2 |
| derived, Hall | C9×C112 ⋊ C2×C5 |
| Hall | C5×C112 ⋊ D9 |
| Sylow | C112 ⋊ C5×D9 |
| Hall | C5×C9 ⋊ C11⋊D11 |
| Sylow | C9 ⋊ C5×C11⋊D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C9⋊(C11⋊D11) |
| commutator, cosocle, hypocenter | C9×C112 | C2×C5 |
| Frattini | C3 | C5×C3⋊(C11⋊D11) |
| Fitting | C5×C9×C112 | C2 |
| socle | C3×C5×C112 | D3 |
| LCS | G ▷ C9×C112 | |
| UCS | C1 ◁ C5 | |
168 conjugacy classes of subgroups.
2730 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D9×C11⋊D11, C5×D11×D99, D5×C9⋊(C11⋊D11), … |
| maximal normal subgroup of | C5×D9×C11⋊D11, C5×D11×D99, D5×C9⋊(C11⋊D11), … |
| maximal quotient of | C5×C9⋊(C11⋊Dic11), C2×C5×C9⋊(C11⋊D11) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 78);