Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊(C67⋊#261) |
| unambiguous semidirect product | C67⋊(C9⋊#261) |
| Fitting, derived, Hall | C9×C13×C67 ⋊ C4 |
| Hall | C13×C67 ⋊ Dic9 |
| Hall | C9×C67 ⋊ #261 |
| Hall | C9×C13 ⋊ Dic67 |
| Sylow | C67 ⋊ C9⋊#261 |
| Sylow | C13 ⋊ Dic603 |
| Sylow | C9 ⋊ C67⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C9×C13×C67 | C4 |
| Frattini | C3 | C3⋊(C67⋊#261) |
| socle | C3×C13×C67 | Dic3 |
| prime radical | C3×D13×C67 | D3 |
| cosocle | C9×D13×C67 | C2 |
| LCS | G ▷ C9×C13×C67 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7839 |
Polycyclic presentation:
2^2,3,13,67,3|a^2=b,c^3=f^2,c^a=c^2f,d^a=d^5,e^a=e^66,f^a=f^2,d^b=d^122415 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 55);