Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#11923885 |
| unambiguous semidirect product | C3⋊(C3×#11923885) |
| Fitting, socle, Hall | C32×C172 ⋊ C4 |
| derived | C3×C172 ⋊ C3×C4 |
| Sylow | C172 ⋊ C3×Dic3 |
| Sylow | C32 ⋊ #11923885 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊#11923885 |
| commutator, hypocenter | C3×C172 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C172 | C4 |
| prime radical | C32×C17×D17 | C2 |
| cosocle | C3×C17×D17 | C2×C3 |
| LCS | G ▷ C3×C172 | |
| UCS | C1 ◁ C3 | |
80 conjugacy classes of subgroups.
774 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 123);