Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of C3⋊(C3⋊D63) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C33 |
| unambiguous semidirect product | C3⋊(C3⋊D63) |
| unambiguous semidirect product | C7⋊(C3⋊(C3⋊D9)) |
| unambiguous semidirect product | C9⋊(C3⋊D21) |
| Fitting, derived, Hall | C32×C7×C9 ⋊ C2 |
| Sylow | C32×C9 ⋊ D7 |
| Sylow | C7 ⋊ C3⋊(C3⋊D9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C7×C9 | C2 |
| Frattini | C3 | C3⋊(C3⋊D21) |
| socle | C33×C7 | D3 |
| LCS | G ▷ C32×C7×C9 | |
| UCS | C1 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 567 |
Polycyclic presentation:
2,3^3,7,3|d^3=f^2,b^a=b^2,c^a=c^2,d^a=d^2f,e^a=e^6,f^a=f^2285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 231);