Finite Group DatabasebetaFinite Group Databasebeta| order | 6138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D279 |
| unambiguous semidirect product | C9⋊(C11×D31) |
| unambiguous semidirect product | C31⋊(C11×D9) |
| Fitting, Hall | C9×C11×C31 ⋊ C2 |
| derived, Hall | C9×C31 ⋊ C2×C11 |
| Hall | C11×C31 ⋊ D9 |
| Hall | C9×C11 ⋊ D31 |
| Sylow | C31 ⋊ C11×D9 |
| Sylow | C9 ⋊ C11×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D279 |
| commutator, hypocenter | C9×C31 | C2×C11 |
| Frattini | C3 | C11×D93 |
| Fitting | C9×C11×C31 | C2 |
| socle | C3×C11×C31 | D3 |
| LCS | G ▷ C9×C31 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
1551 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D9×D31, D11×D279, D99⋊D31, … |
| maximal normal subgroup of | C11×D9×D31, D11×D279, D99⋊D31, … |
| maximal quotient of | C11×Dic279, C2×C11×D279, C5×C11×D279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6138, 7);