Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊#11923876) |
| Fitting, derived, Hall | C32×C289 ⋊ C4 |
| Sylow | C289 ⋊ C3⋊Dic3 |
| Sylow | C32 ⋊ #11923876 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C32×C289 | C4 |
| Frattini | C17 | C3⋊(C3⋊#595) |
| socle | C32×C17 | #595 |
| prime radical, cosocle | C32×D289 | C2 |
| LCS | G ▷ C32×C289 | |
| UCS | C1 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,17^2|a^2=b,e^17=f^9,c^a=c^2,d^a=d^2,e^a=e^4f,f^a=f^4,e^b=e^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, 22);