Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Hall | C32×C289 ⋊ C4 |
| Sylow | C289 ⋊ #157 |
| Sylow | C32 ⋊ Dic289 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C32×C289 | C4 |
| Frattini | C17 | #10597480 |
| socle | C32×C17 | Dic17 |
| prime radical | C17×C3⋊D3 | D17 |
| cosocle | C3⋊D3×C289 | C2 |
| LCS | G ▷ C32×C289 | |
| UCS | C1 | |
30 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,17^2|a^2=b,e^17=f^16,c^a=d,d^a=c^2,e^a=e^16f,f^a=f^16,c^b=c^2,d^b=d^2870 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 25);