Finite Group DatabasebetaFinite Group Databasebeta| order | 594 |
| isoclinism | isoclinic class of D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | C33×D11 |
| unambiguous semidirect product | C11⋊(C2×C33) |
| Fitting, socle, Hall | C33×C11 ⋊ C2 |
| derived, Sylow | C11 ⋊ C2×C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | D11 |
| commutator, cosocle, hypocenter | C11 | C2×C33 |
| Frattini | C1 | G |
| Fitting, socle | C33×C11 | C2 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C33 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 297 |
189 conjugacy classes — view the full character table.
| maximal subgroup of | C32×D3×D11, C3×C3⋊D3×D11, D11×C3⋊(C3⋊D3), … |
| maximal normal subgroup of | C32×D3×D11, C3×C3⋊D3×D11, D11×C3⋊(C3⋊D3), … |
| maximal quotient of | C33×Dic11, C2×C33×D11, C32×C9×D11, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(594, 23);