Finite Group DatabasebetaFinite Group Databasebeta| order | 9477 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C13 · Schur multiplier (H2) = C32 |
| direct product | H(3,𝔽3)×C33⋊C13 |
| unambiguous semidirect product | C32⋊(C3×C33⋊C13) |
| unambiguous semidirect product | (C33×H(3,𝔽3))⋊C13 |
| Fitting, Sylow | C33×H(3,𝔽3) ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×C33⋊C13 |
| commutator, socle, cosocle | C34 | C32×C13 |
| Fitting | C33×H(3,𝔽3) | C13 |
| hypercenter | H(3,𝔽3) | C33⋊C13 |
| hypocenter | C33 | C13×H(3,𝔽3) |
| LCS | G ▷ C34 ▷ C33 | |
| UCS | C1 ◁ C3 ◁ H(3,𝔽3) | |
494 conjugacy classes of subgroups.
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9477, 4038);