Finite Group DatabasebetaFinite Group Databasebeta| order | 5598 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C311 · Schur multiplier (H2) = C1 |
| direct product | D9×C311 |
| unambiguous semidirect product | C9⋊(C2×C311) |
| Fitting, Hall | C9×C311 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C311 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C311 | D9 |
| commutator, hypocenter | C9 | C2×C311 |
| Frattini | C3 | D3×C311 |
| Fitting | C9×C311 | C2 |
| socle | C3×C311 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C311 | |
12 conjugacy classes of subgroups.
1866 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D311, C2×D9×C311, C5×D9×C311, … |
| maximal normal subgroup of | D9×D311, C2×D9×C311, C5×D9×C311, … |
| maximal quotient of | Dic9×C311, C2×D9×C311, C5×D9×C311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5598, 2);