Finite Group DatabasebetaFinite Group Databasebeta| order | 8343 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | C32⋊(C103⋊C9) |
| Sylow | C103 ⋊ C32⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C3×C103⋊C3 |
| commutator | C3×C103 | C3×C9 |
| Fitting | C33×C103 | C3 |
| socle | C32×C103 | C32 |
| hypercenter | C33 | C103⋊C3 |
| hypocenter | C103 | C32⋊C9 |
| LCS | G ▷ C3×C103 ▷ C103 | |
| UCS | C1 ◁ C32 ◁ C33 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
3^4,103|a^3=d,b^a=bc,e^a=e^56951 conjugacy classes — view the full character table.
| maximal subgroup of | #38736421, #38736422, #38736423, … |
| maximal normal subgroup of | #38736421, #38736422, #38736423, … |
| maximal quotient of | C103⋊#6855, C32⋊(C103⋊C27), #38736447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8343, 19);