Finite Group DatabasebetaFinite Group Databasebeta| order | 10404 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C17 |
| direct product | Dic3×C172⋊C3 |
| unambiguous semidirect product | C3⋊(C4×C172⋊C3) |
| unambiguous semidirect product | (Dic3×C172)⋊C3 |
| derived | C3×C172 ⋊ C3×C4 |
| Hall | C3×C172⋊C3 ⋊ C4 |
| Sylow | C172 ⋊ C3×Dic3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C172⋊C3 |
| commutator, hypocenter | C3×C172 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C172 | C2×C3 |
| prime radical | C2×C3×C172⋊C3 | C2 |
| LCS | G ▷ C3×C172 | |
| UCS | C1 ◁ C2 | |
64 conjugacy classes of subgroups.
594 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10404, 81);