Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C35 |
No aliases for this group.
| Fitting | C3×C43×AΣL(1,𝔽27) ⋊ C3 |
| Sylow | C43 ⋊ UT(4,𝔽3) |
560 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1161 |
Polycyclic presentation:
3^6,43|b^a=bd,c^a=ce,d^a=df,g^a=g^36,e^b=ef,g^b=g^6,d^c=df,g^c=g^36771 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 2346);