Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×#11923876 |
| Fitting, Hall | C32×C289 ⋊ C4 |
| derived, Sylow | C289 ⋊ C32×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #11923876 |
| commutator, hypocenter | C289 | C32×C4 |
| Frattini | C17 | C32×#595 |
| Fitting | C32×C289 | C4 |
| socle | C32×C17 | #595 |
| prime radical | C32×D289 | C2 |
| cosocle | D289 | C2×C32 |
| LCS | G ▷ C289 | |
| UCS | C1 ◁ C32 | |
54 conjugacy classes of subgroups.
684 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 20);