Finite Group DatabasebetaFinite Group Databasebeta| order | 31434 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C132 · Schur multiplier (H2) = C13 |
| direct product | C132×D31⋊C3 |
| unambiguous semidirect product | D31⋊(C3×C132) |
| unambiguous semidirect product | (C31⋊C3)⋊(C2×C132) |
| Fitting, socle, Hall | C132×C31 ⋊ C2×C3 |
| derived, Sylow | C31 ⋊ C2×C3×C132 |
| Hall | C132×C31⋊C3 ⋊ C2 |
| Hall | C132×D31 ⋊ C3 |
| Hall | C31⋊C3 ⋊ C2×C132 |
| Hall | D31 ⋊ C3×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | D31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C2×C3×C132 |
| Frattini | C1 | G |
| Fitting, socle | C132×C31 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C132 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5239 |
1859 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31434, 28);