Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊D243 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D243 |
| unambiguous semidirect product | C243⋊D3 |
| Fitting, derived, Sylow | C3×C243 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C243 | C2 |
| Frattini | C81 | C3⋊D3 |
| socle | C32 | D81 |
| LCS | G ▷ C3×C243 | |
| UCS | C1 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 729 |
Polycyclic presentation:
2,3^6|b^3=d,d^3=e,e^3=f,f^3=g,b^a=b^2d^2e^2f^2g^2,c^a=c^2,d^a=d^2e^2f^2g^2,e^a=e^2f^2g^2,f^a=f^2g^2,g^a=g^2366 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 656);