Finite Group DatabasebetaFinite Group Databasebeta| order | 9477 |
| isoclinism | isoclinic class of C33⋊C13 |
| automorphism | ? |
| homology | Abelianization (H1) = C13×C27 · Schur multiplier (H2) = C1 |
| direct product | C27×C33⋊C13 |
| unambiguous semidirect product | (C33×C27)⋊C13 |
| Fitting, Sylow | C33×C27 ⋊ C13 |
| derived | C33 ⋊ C13×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C27 | C33⋊C13 |
| commutator, hypocenter | C33 | C13×C27 |
| Frattini | C9 | C3×C33⋊C13 |
| Fitting | C33×C27 | C13 |
| socle | C34 | C9×C13 |
| prime radical | C3×C33⋊C13 | C9 |
| cosocle | C33×C9 | C3×C13 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C27 | |
60 conjugacy classes of subgroups.
405 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9477, 4036);