Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊((C67⋊C3)⋊Dic13) |
| unambiguous semidirect product | (C67⋊C3)⋊Dic39 |
| derived | C3×C13×C67 ⋊ C3×C4 |
| Hall | C3×C13×C67⋊C3 ⋊ C4 |
| Hall | C13×C67 ⋊ C3×Dic3 |
| Hall | C3×C67⋊C3 ⋊ Dic13 |
| Sylow | C67 ⋊ C3×Dic39 |
| Sylow | C13 ⋊ C3⋊((C67⋊C3)⋊C4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊((C67⋊C3)⋊D13) |
| commutator, hypocenter | C3×C13×C67 | C3×C4 |
| Fitting, socle, cosocle | C2×C3×C13×C67 | C2×C3 |
| prime radical | C2×C3×C13×C67⋊C3 | C2 |
| LCS | G ▷ C3×C13×C67 | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10452 |
Polycyclic presentation:
2,3^2,13,67,2|a^2=f,c^a=c^2,d^a=d^12,e^a=e^66,e^b=e^29984 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 108);