Finite Group DatabasebetaFinite Group Databasebeta| order | 594 |
| isoclinism | isoclinic class of C3⋊D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C3 |
| direct product | C11×C3⋊D9 |
| unambiguous semidirect product | C3⋊(C11×D9) |
| unambiguous semidirect product | C9⋊(D3×C11) |
| Fitting, Hall | C3×C9×C11 ⋊ C2 |
| derived, Sylow | C3×C9 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊D9 |
| commutator, cosocle, hypocenter | C3×C9 | C2×C11 |
| Frattini | C3 | C11×C3⋊D3 |
| Fitting | C3×C9×C11 | C2 |
| socle | C32×C11 | D3 |
| LCS | G ▷ C3×C9 | |
| UCS | C1 ◁ C11 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 297 |
165 conjugacy classes — view the full character table.
| maximal subgroup of | D11×C3⋊D9, D3×C11×D9, (C3⋊D9)⋊D11, … |
| maximal normal subgroup of | D11×C3⋊D9, D3×C11×D9, (C3⋊D9)⋊D11, … |
| maximal quotient of | C11×C3⋊Dic9, C2×C11×C3⋊D9, C11×C9⋊D9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(594, 16);