Finite Group DatabasebetaFinite Group Databasebeta| order | 6138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊(D31⋊C3)) |
| unambiguous semidirect product | C11⋊(C3⋊(D31⋊C3)) |
| unambiguous semidirect product | (C31⋊C3)⋊D33 |
| unambiguous semidirect product | D1023⋊C3 |
| Fitting, socle, derived | C3×C11×C31 ⋊ C2×C3 |
| Hall | C3×C11×C31⋊C3 ⋊ C2 |
| Hall | C11×C31 ⋊ C3×D3 |
| Hall | C3×C31⋊C3 ⋊ D11 |
| Sylow | C31 ⋊ C3×D33 |
| Sylow | C11 ⋊ C3⋊(D31⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C11×C31 | C2×C3 |
| LCS | G ▷ C3×C11×C31 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,11,31|c^a=c^2,d^a=d^10,e^a=e^30,e^b=e^5219 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6138, 19);