Finite Group DatabasebetaFinite Group Databasebeta| order | 9477 |
| automorphism | ? |
| homology | Abelianization (H1) = C13 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | #10624562⋊C13 |
| Fitting, derived, Sylow | #10624562 ⋊ C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | #10624562 | C13 |
| Frattini, socle | C33 | C33⋊C13 |
| LCS | G ▷ #10624562 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
Polycyclic presentation:
13,3^6|b^a=bcdef^2g,c^a=bd^2g,d^a=bc^2d^2ef^2,e^a=e^2fg^2,f^a=ef,g^a=e^2g^2,c^b=ce,d^b=df,d^c=dg21 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9477, 4035);