Finite Group DatabasebetaFinite Group Databasebeta| order | 1809 |
| isoclinism | isoclinic class of C67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×C67⋊C9 |
| unambiguous semidirect product | (C3×C67)⋊C9 |
| derived, Sylow | C67 ⋊ C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | C67⋊C3 |
| commutator, hypocenter | C67 | C3×C9 |
| Frattini | C3 | C3×C67⋊C3 |
| Fitting, socle, prime radical | C32×C67 | C3 |
| cosocle | C3×C67 | C32 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C32 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1809 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1809, 8);