Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C33×C9 |
No aliases for this group.
| Fitting | C43×#6898 ⋊ C3 |
| Sylow | C43 ⋊ #10624913 |
596 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 250 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=ef,b^3=e^2,b^a=be,c^a=cf,d^a=def,c^b=ce^2f,d^b=de,g^d=g^36803 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 3837);