Finite Group DatabasebetaFinite Group Databasebeta| order | 31242 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C127 · Schur multiplier (H2) = C1 |
| direct product | C127×D123 |
| unambiguous semidirect product | C3⋊(D41×C127) |
| unambiguous semidirect product | C41⋊(D3×C127) |
| Fitting, socle, Hall | C3×C41×C127 ⋊ C2 |
| derived, Hall | C3×C41 ⋊ C2×C127 |
| Hall | C41×C127 ⋊ D3 |
| Hall | C3×C127 ⋊ D41 |
| Sylow | C41 ⋊ D3×C127 |
| Sylow | C3 ⋊ D41×C127 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C127 | D123 |
| commutator, cosocle, hypocenter | C3×C41 | C2×C127 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C127 | C2 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C127 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15621 |
8001 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31242, 8);