Finite Group DatabasebetaFinite Group Databasebeta| order | 1134 |
| isoclinism | isoclinic class of C3⋊(C3⋊(C3⋊D21)) |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C36 |
| unambiguous semidirect product | C3⋊(C3⋊(C3⋊D21)) |
| unambiguous semidirect product | C7⋊(C3⋊(C3⋊(C3⋊D3))) |
| Fitting, socle, derived, Hall | C34×C7 ⋊ C2 |
| Sylow | C34 ⋊ D7 |
| Sylow | C7 ⋊ C3⋊(C3⋊(C3⋊D3)) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C34×C7 | C2 |
| LCS | G ▷ C34×C7 | |
| UCS | C1 | |
848 conjugacy classes of subgroups.
| transitive degree | μt(G) = 567 |
Polycyclic presentation:
2,3^4,7|b^a=b^2,c^a=c^2,d^a=d^2,e^a=e^2,f^a=f^6285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1134, 253);