Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C43×C9⋊H(3,𝔽3) ⋊ C3 |
| Sylow | C43 ⋊ #10624601 |
232 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 58 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=f,c^3=e,b^a=bd,c^a=ce,d^a=de,g^a=g^6,d^b=df,g^b=g^36787 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 1170);