Finite Group DatabasebetaFinite Group Databasebeta| order | 10890 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C112 · Schur multiplier (H2) = C11 |
| direct product | C112×D45 |
| unambiguous semidirect product | C5⋊(C112×D9) |
| unambiguous semidirect product | C9⋊(D5×C112) |
| Fitting, Hall | C5×C9×C112 ⋊ C2 |
| derived, Hall | C5×C9 ⋊ C2×C112 |
| Hall | C9×C112 ⋊ D5 |
| Hall | C5×C112 ⋊ D9 |
| Sylow | C9 ⋊ D5×C112 |
| Sylow | C5 ⋊ C112×D9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C112 | D45 |
| commutator, cosocle, hypocenter | C5×C9 | C2×C112 |
| Frattini | C3 | C112×D15 |
| Fitting | C5×C9×C112 | C2 |
| socle | C3×C5×C112 | D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C112 | |
168 conjugacy classes of subgroups.
2904 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D11×D45, D45×C11⋊D11, D5×C112×D9, … |
| maximal normal subgroup of | C11×D11×D45, D45×C11⋊D11, D5×C112×D9, … |
| maximal quotient of | C112×Dic45, C2×C112×D45 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10890, 79);