Finite Group DatabasebetaFinite Group Databasebeta| order | 9477 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C13×C27 · Schur multiplier (H2) = C32 |
| direct product | C3×C13×C81⋊C3 |
| unambiguous semidirect product | C81⋊(C32×C13) |
| subgroup | G/H | |
|---|---|---|
| center | C3×C13×C27 | C32 |
| commutator | C3 | C32×C13×C27 |
| Frattini, cosocle | C27 | C33×C13 |
| socle | C32×C13 | C3×C27 |
| prime radical | C33×C13 | C27 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C13×C27 ◁ G | |
164 conjugacy classes of subgroups.
3861 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9477, 392);