Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C67⋊#90866 |
| Fitting, socle, derived, Hall | C32×C13×C67 ⋊ C4 |
| Hall | C13×C67 ⋊ #157 |
| Hall | C32×C67 ⋊ #261 |
| Hall | C32×C13 ⋊ Dic67 |
| Sylow | C67 ⋊ #90866 |
| Sylow | C13 ⋊ C67⋊#157 |
| Sylow | C32 ⋊ C67⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C13×C67 | C4 |
| prime radical, cosocle | C67×C3⋊D39 | C2 |
| LCS | G ▷ C32×C13×C67 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5226 |
Polycyclic presentation:
2^2,3^2,13,67|a^2=b,c^a=cd,d^a=cd^2,e^a=e^5,f^a=f^66,c^b=c^2,d^b=d^2,e^b=e^122013 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 216);