Finite Group DatabasebetaFinite Group Databasebeta| order | 31218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×D43⋊C3 |
| unambiguous semidirect product | D43⋊(C3×C121) |
| unambiguous semidirect product | (C43⋊C3)⋊(C2×C121) |
| unambiguous semidirect product | (D43×C121)⋊C3 |
| Fitting, Hall | C43×C121 ⋊ C2×C3 |
| derived, Sylow | C43 ⋊ C2×C3×C121 |
| Hall | C121×C43⋊C3 ⋊ C2 |
| Hall | D43×C121 ⋊ C3 |
| Hall | C43⋊C3 ⋊ C2×C121 |
| Hall | D43 ⋊ C3×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | D43⋊C3 |
| commutator, hypocenter | C43 | C2×C3×C121 |
| Frattini | C11 | C11×D43⋊C3 |
| Fitting | C43×C121 | C2×C3 |
| socle, cosocle | C11×C43 | C2×C3×C11 |
| prime radical | C11×D43⋊C3 | C11 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C121 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5203 |
1573 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31218, 10);