Finite Group DatabasebetaFinite Group Databasebeta| order | 8343 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | 3−1+2×C103 ⋊ C3 |
| Sylow | C103 ⋊ AΣL(1,𝔽27) |
40 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,103|b^a=bc,c^a=cd,e^a=e^46,e^b=e^56391 conjugacy classes — view the full character table.
| maximal subgroup of | AΣL(1,𝔽27)×C103⋊C3, C3×#22552463, #38736609, … |
| maximal normal subgroup of | AΣL(1,𝔽27)×C103⋊C3, C3×#22552463, #38736609, … |
| maximal quotient of | #38736422, #38736423, #38736425, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8343, 30);