Finite Group DatabasebetaFinite Group Databasebeta| order | 31356 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊(D13⋊C3))⋊D67 |
| unambiguous semidirect product | ((C13⋊C3)⋊D67)⋊D3 |
| Fitting, socle, derived | C3×C13×C67 ⋊ C22×C3 |
| Hall | C3×C13⋊C3×C67 ⋊ C22 |
| Hall | C13×C67 ⋊ C2×C3×D3 |
| Hall | C3×C13⋊C3 ⋊ C2×D67 |
| Sylow | C67 ⋊ D3×D13⋊C3 |
| Sylow | C13 ⋊ C3×D3×D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C67 | C22×C3 |
| LCS | G ▷ C3×C13×C67 | |
| UCS | C1 | |
88 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2613 |
Polycyclic presentation:
2^2,3^2,13,67|e^a=e^12,f^a=f^66,d^b=d^2,e^b=e^12,e^c=e^3519 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31356, 165);