Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | 3−1+2⋊(C43⋊C27) |
| Sylow | C43 ⋊ 3−1+2⋊C27 |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10449 |
Polycyclic presentation:
3^6,43|a^3=d,b^3=e,d^3=f,b^a=bc,c^a=ce,g^a=g^36,c^b=ce1539 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 520);