Finite Group DatabasebetaFinite Group Databasebeta| order | 6498 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C361 · Schur multiplier (H2) = C1 |
| direct product | C3×D3×C361 |
| unambiguous semidirect product | C3⋊(C2×C3×C361) |
| Fitting, Hall | C32×C361 ⋊ C2 |
| derived | C3 ⋊ C2×C3×C361 |
| Sylow | C32 ⋊ C2×C361 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C361 | D3 |
| commutator, hypocenter | C3 | C2×C3×C361 |
| Frattini | C19 | C3×D3×C19 |
| Fitting | C32×C361 | C2 |
| socle | C32×C19 | C2×C19 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C3×C361 | |
27 conjugacy classes of subgroups.
3249 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×D361, D32×C361, D3×D1083, … |
| maximal normal subgroup of | C3×D3×D361, D32×C361, D3×D1083, … |
| maximal quotient of | C3×Dic3×C361, C2×C3×D3×C361, C3×C5×D3×C361, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6498, 15);