Finite Group DatabasebetaFinite Group Databasebeta| order | 594 |
| isoclinism | isoclinic class of C3⋊(C3⋊D3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C33 |
| direct product | C11×C3⋊(C3⋊D3) |
| unambiguous semidirect product | C3⋊(C11×C3⋊D3) |
| Fitting, socle, Hall | C33×C11 ⋊ C2 |
| derived, Sylow | C33 ⋊ C2×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C3⋊(C3⋊D3) |
| commutator, cosocle, hypocenter | C33 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C33×C11 | C2 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C11 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 297 |
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(594, 28);