Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#23782989 |
| Fitting, socle, derived | C3×C13×C67 ⋊ C3×C4 |
| Hall | C3×C13⋊C3×C67 ⋊ C4 |
| Hall | C13×C67 ⋊ C3×Dic3 |
| Hall | C3×C13⋊C3 ⋊ Dic67 |
| Sylow | C67 ⋊ C3⋊AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×Dic201 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C67 | C3×C4 |
| prime radical | C3×C67×D13⋊C3 | C2 |
| cosocle | C3×D13×C67 | C2×C3 |
| LCS | G ▷ C3×C13×C67 | |
| UCS | C1 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2613 |
Polycyclic presentation:
2,3,2,3,13,67|a^2=c,d^a=d^2,e^a=e^5,f^a=f^66,e^b=e^9,e^c=e^12813 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 150);