Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C27 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | #11923956⋊C27 |
| Fitting | C43×C9⋊C27 ⋊ C3 |
| Sylow | C43 ⋊ C27×3−1+2 |
220 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10449 |
Polycyclic presentation:
3^6,43|a^3=e,b^3=d,c^3=e,e^3=f,b^a=bd,g^c=g^361683 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 2219);