Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊#11923876 |
| Fitting, derived, Hall | C9×C289 ⋊ C4 |
| Sylow | C289 ⋊ Dic9 |
| Sylow | C9 ⋊ #11923876 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C289 | C4 |
| Frattini, socle | C3×C17 | C3⋊#595 |
| prime radical | C3×D289 | D3 |
| cosocle | C9×D289 | C2 |
| LCS | G ▷ C9×C289 | |
| UCS | C1 | |
27 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,17,3,17|a^2=b,c^3=e^2,d^17=f^9,c^a=c^2e,d^a=d^4f,e^a=e^2,f^a=f^4,d^b=d^16f^8,f^b=f^16660 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 7);