Finite Group DatabasebetaFinite Group Databasebeta| order | 6138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D341 |
| unambiguous semidirect product | C11⋊(C32×D31) |
| Fitting, socle, Hall | C32×C11×C31 ⋊ C2 |
| derived, Hall | C11×C31 ⋊ C2×C32 |
| Hall | C32×C31 ⋊ D11 |
| Hall | C32×C11 ⋊ D31 |
| Sylow | C31 ⋊ C32×D11 |
| Sylow | C11 ⋊ C32×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D341 |
| commutator, hypocenter | C11×C31 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C11×C31 | C2 |
| LCS | G ▷ C11×C31 | |
| UCS | C1 ◁ C32 | |
48 conjugacy classes of subgroups.
1548 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×D11×D31, C3×D3×D341, C3×D33⋊D31, … |
| maximal normal subgroup of | C32×D11×D31, C3×D3×D341, C3×D33⋊D31, … |
| maximal quotient of | C32×Dic341, C2×C32×D341, C32×C5×D341, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6138, 24);