Finite Group DatabasebetaFinite Group Databasebeta| order | 594 |
| isoclinism | isoclinic class of C3⋊D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C3 |
| direct product | C3×C3⋊D33 |
| unambiguous semidirect product | C3⋊(C3×D33) |
| unambiguous semidirect product | C11⋊(C3×C3⋊D3) |
| Fitting, socle, Hall | C33×C11 ⋊ C2 |
| derived | C32×C11 ⋊ C2×C3 |
| Sylow | C33 ⋊ D11 |
| Sylow | C11 ⋊ C3×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊D33 |
| commutator, cosocle, hypocenter | C32×C11 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C33×C11 | C2 |
| LCS | G ▷ C32×C11 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 198 |
153 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C3⋊D3×D11, C3×D3×D33, D3×C3⋊D33, … |
| maximal normal subgroup of | C3×C3⋊D3×D11, C3×D3×D33, D3×C3⋊D33, … |
| maximal quotient of | C3×C3⋊Dic33, C2×C3×C3⋊D33, C3×C3⋊D99, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(594, 27);