Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| isoclinism | isoclinic class of C3⋊(C9⋊D27) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C32×C9 |
| unambiguous semidirect product | C3⋊(C9⋊D27) |
| unambiguous semidirect product | C9⋊(C3⋊D27) |
| unambiguous semidirect product | C27⋊(C3⋊D9) |
| Fitting, derived, Sylow | C3×C9×C27 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C9×C27 | C2 |
| Frattini | C3×C9 | C3⋊(C3⋊D3) |
| socle | C33 | C3⋊D9 |
| LCS | G ▷ C3×C9×C27 | |
| UCS | C1 | |
404 conjugacy classes of subgroups.
| transitive degree | μt(G) = 729 |
Polycyclic presentation:
2,3^6|b^3=e,c^3=f,e^3=g,b^a=b^2e^2g^2,c^a=c^2f^2,d^a=d^2,e^a=e^2g^2,f^a=f^2,g^a=g^2366 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 933);