Finite Group DatabasebetaFinite Group Databasebeta| order | 31347 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C43 ⋊ #10624577 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C33 | C32×C43⋊C3 |
| commutator, socle, prime radical, cosocle | C33×C43 | C33 |
| Fitting | C43×#6855 | C3 |
| hypercenter | #6855 | C43⋊C3 |
| hypocenter | C43 | #10624577 |
| LCS | G ▷ C33×C43 ▷ C43 | |
| UCS | C1 ◁ C33 ◁ #6855 | |
296 conjugacy classes of subgroups.
| transitive degree | μt(G) = 31347 |
Polycyclic presentation:
3^6,43|a^3=def,b^3=de^2,c^3=d,b^a=bd,c^a=ce,g^a=g^36,c^b=cf,g^b=g^36,g^c=g^61491 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31347, 1040);