Finite Group DatabasebetaFinite Group Databasebeta| order | 31218 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C43⋊C3×D121 |
| unambiguous semidirect product | C121⋊(C2×C43⋊C3) |
| unambiguous semidirect product | (C43×D121)⋊C3 |
| Fitting, derived, Hall | C43×C121 ⋊ C2×C3 |
| Hall | C121×C43⋊C3 ⋊ C2 |
| Hall | C43×D121 ⋊ C3 |
| Sylow | C121 ⋊ C2×C43⋊C3 |
| Sylow | C43 ⋊ C3×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C43×C121 | C2×C3 |
| Frattini | C11 | D11×C43⋊C3 |
| socle | C11×C43 | C3×D11 |
| LCS | G ▷ C43×C121 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5203 |
1054 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31218, 11);