Finite Group DatabasebetaFinite Group Databasebeta| order | 31242 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D127⋊C3 |
| unambiguous semidirect product | D127⋊(C3×C41) |
| unambiguous semidirect product | (C127⋊C3)⋊(C2×C41) |
| unambiguous semidirect product | (C41×D127)⋊C3 |
| Fitting, socle, Hall | C41×C127 ⋊ C2×C3 |
| derived, Sylow | C127 ⋊ C2×C3×C41 |
| Hall | C41×C127⋊C3 ⋊ C2 |
| Hall | C41×D127 ⋊ C3 |
| Hall | C127⋊C3 ⋊ C2×C41 |
| Hall | D127 ⋊ C3×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D127⋊C3 |
| commutator, cosocle, hypocenter | C127 | C2×C3×C41 |
| Frattini | C1 | G |
| Fitting, socle | C41×C127 | C2×C3 |
| LCS | G ▷ C127 | |
| UCS | C1 ◁ C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5207 |
1107 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31242, 10);