Finite Group DatabasebetaFinite Group Databasebeta| order | 8343 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | H(3,𝔽3)×C103 ⋊ C3 |
| Sylow | C103 ⋊ #732 |
32 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,103|b^3=d^2,b^a=bc,c^a=cd,e^b=e^56391 conjugacy classes — view the full character table.
| maximal subgroup of | #732×C103⋊C3, C3×#22552467, #38736608, … |
| maximal normal subgroup of | #732×C103⋊C3, C3×#22552467, #38736608, … |
| maximal quotient of | #38736421, #38736422, #38736430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8343, 34);