Finite Group DatabasebetaFinite Group Databasebeta| order | 990 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×C9×D11 |
| Fitting, Hall | C5×C9×C11 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C5×C9 |
| Hall | C9×C11 ⋊ C2×C5 |
| Hall | C5×C11 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C9 | D11 |
| commutator, hypocenter | C11 | C2×C5×C9 |
| Frattini | C3 | C3×C5×D11 |
| Fitting | C5×C9×C11 | C2 |
| socle | C3×C5×C11 | C2×C3 |
| prime radical | C3×C5×D11 | C3 |
| cosocle | C3×C11 | C2×C3×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C5×C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 495 |
315 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D5×D11, C5×D9×D11, D11×D45, … |
| maximal normal subgroup of | C9×D5×D11, C5×D9×D11, D11×D45, … |
| maximal quotient of | C5×C9×Dic11, C2×C5×C9×D11, C5×C9×D121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(990, 5);