Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C38 |
| unambiguous semidirect product | C43⋊#10624562 |
| Fitting | C32×H(3,𝔽3)×C43 ⋊ C3 |
| Sylow | C43 ⋊ #10624562 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C33 | C32×C43⋊C3 |
| commutator, socle, cosocle | C33×C43 | C33 |
| Fitting | C32×H(3,𝔽3)×C43 | C3 |
| hypercenter | C32×H(3,𝔽3) | C43⋊C3 |
| hypocenter | C43 | #10624562 |
| LCS | G ▷ C33×C43 ▷ C43 | |
| UCS | C1 ◁ C33 ◁ C32×H(3,𝔽3) | |
2138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10449 |
Polycyclic presentation:
3^6,43|b^a=bd,c^a=ce,c^b=cf,g^c=g^361491 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 951);