Finite Group DatabasebetaFinite Group Databasebeta| order | 990 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C11 · Schur multiplier (H2) = C1 |
| direct product | C5×C11×D9 |
| unambiguous semidirect product | C9⋊(C2×C5×C11) |
| Fitting, Hall | C5×C9×C11 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C5×C11 |
| Hall | C9×C11 ⋊ C2×C5 |
| Hall | C5×C9 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C11 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C5×C11 |
| Frattini | C3 | C5×D3×C11 |
| Fitting | C5×C9×C11 | C2 |
| socle | C3×C5×C11 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C5×C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 495 |
330 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D9×D11, D5×C11×D9, D9×D55, … |
| maximal normal subgroup of | C5×D9×D11, D5×C11×D9, D9×D55, … |
| maximal quotient of | C5×C11×Dic9, C2×C5×C11×D9, C5×D9×C121, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(990, 8);