Finite Group DatabasebetaFinite Group Databasebeta| order | 594 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
| direct product | D11×3−1+2 |
| unambiguous semidirect product | C11⋊(C2×3−1+2) |
| unambiguous semidirect product | (C9×D11)⋊C3 |
| Fitting, Hall | C11×3−1+2 ⋊ C2 |
| Sylow | C11 ⋊ C2×3−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×D11 |
| commutator, socle, cosocle | C3×C11 | C2×C32 |
| Fitting | C11×3−1+2 | C2 |
| prime radical | C32×D11 | C3 |
| hypercenter | 3−1+2 | D11 |
| hypocenter | C11 | C2×3−1+2 |
| LCS | G ▷ C3×C11 ▷ C11 | |
| UCS | C1 ◁ C3 ◁ 3−1+2 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 99 |
77 conjugacy classes — view the full character table.
| maximal subgroup of | D11×AGL(1,ℤ/9), C2×D11×3−1+2, D11×AΣL(1,𝔽27), … |
| maximal normal subgroup of | D11×AGL(1,ℤ/9), C2×D11×3−1+2, D11×AΣL(1,𝔽27), … |
| maximal quotient of | 3−1+2×Dic11, C2×D11×3−1+2, D11×C32⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(594, 7);