Finite Group DatabasebetaFinite Group Databasebeta| order | 594 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×C9×D11 |
| unambiguous semidirect product | C11⋊(C2×C3×C9) |
| Fitting, Hall | C3×C9×C11 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C9 | D11 |
| commutator, hypocenter | C11 | C2×C3×C9 |
| Frattini | C3 | C32×D11 |
| Fitting | C3×C9×C11 | C2 |
| socle | C32×C11 | C2×C3 |
| prime radical | C32×D11 | C3 |
| cosocle | C3×C11 | C2×C32 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C3×C9 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 297 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D9×D11, D3×C9×D11, D11×C3⋊D9, … |
| maximal normal subgroup of | C3×D9×D11, D3×C9×D11, D11×C3⋊D9, … |
| maximal quotient of | C3×C9×Dic11, C2×C3×C9×D11, C92×D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(594, 5);