Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| Fitting, socle, derived, Hall | C13×C67 ⋊ C32×C4 |
| Hall | C13⋊C3×C67⋊C3 ⋊ C4 |
| Hall | C67⋊#261 ⋊ C32 |
| Sylow | C67 ⋊ C3×AGL(1,𝔽13) |
| Sylow | C13 ⋊ C3×(C67⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C67 | C32×C4 |
| prime radical | D13⋊C3×C67⋊C3 | C2 |
| cosocle | D13×C67 | C2×C32 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 871 |
Polycyclic presentation:
2,3^2,2,13,67|a^2=d,e^a=e^5,f^a=f^66,f^b=f^29,e^c=e^3,e^d=e^12127 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 126);