Finite Group DatabasebetaFinite Group Databasebeta| order | 31434 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C13 |
| unambiguous semidirect product | C3⋊(C13⋊D403) |
| unambiguous semidirect product | C13⋊D1209 |
| unambiguous semidirect product | C31⋊(C3⋊(C13⋊D13)) |
| Fitting, socle, derived, Hall | C3×C132×C31 ⋊ C2 |
| Hall | C132×C31 ⋊ D3 |
| Hall | C3×C132 ⋊ D31 |
| Sylow | C132 ⋊ D93 |
| Hall | C3×C31 ⋊ C13⋊D13 |
| Sylow | C31 ⋊ C3⋊(C13⋊D13) |
| Sylow | C3 ⋊ C13⋊D403 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C132×C31 | C2 |
| LCS | G ▷ C3×C132×C31 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15717 |
Polycyclic presentation:
2,3,13^2,31|b^a=b^2,c^a=c^12,d^a=d^12,e^a=e^307860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31434, 100);