Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C43×3−1+2⋊C9 ⋊ C3 |
| Sylow | C43 ⋊ AΣL(1,𝔽27)⋊C9 |
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3483 |
Polycyclic presentation:
3^6,43|a^3=e,c^3=e,b^a=bd,d^a=df,c^b=cf,g^b=g^6,g^c=g^36819 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 2167);