Finite Group DatabasebetaFinite Group Databasebeta| order | 9477 |
| automorphism | ? |
| homology | Abelianization (H1) = C13 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C93⋊C13 |
| Fitting, derived, Sylow | C93 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C93 | C13 |
| Frattini, socle | C33 | C33⋊C13 |
| LCS | G ▷ C93 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
13,3^6|b^3=e,c^3=f,d^3=g,b^a=bcde^2f^2g,c^a=b^2d^2f^2g^2,d^a=bd^2efg^2,e^a=efg,f^a=e^2g^2,g^a=eg^269 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9477, 4034);