Finite Group DatabasebetaFinite Group Databasebeta| order | 594 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D33 |
| unambiguous semidirect product | C3⋊(C9×D11) |
| unambiguous semidirect product | C11⋊(D3×C9) |
| Fitting, Hall | C3×C9×C11 ⋊ C2 |
| derived | C3×C11 ⋊ C2×C9 |
| Sylow | C3×C9 ⋊ D11 |
| Sylow | C11 ⋊ D3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D33 |
| commutator, hypocenter | C3×C11 | C2×C9 |
| Frattini | C3 | C3×D33 |
| Fitting | C3×C9×C11 | C2 |
| socle, cosocle | C32×C11 | C2×C3 |
| prime radical | C3×D33 | C3 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C9 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C9×D11, D9×D33, (C3⋊D9)⋊D11, … |
| maximal normal subgroup of | D3×C9×D11, D9×D33, (C3⋊D9)⋊D11, … |
| maximal quotient of | C9×Dic33, C2×C9×D33, C9×D99, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(594, 13);