Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C35 |
No aliases for this group.
| Fitting | C32×3−1+2×C43 ⋊ C3 |
| Sylow | C43 ⋊ #10624745 |
500 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 82 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=f^2,b^3=f,b^a=bd,c^a=ce,d^a=df,g^a=g^36,d^b=df1459 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 2330);