Finite Group DatabasebetaFinite Group Databasebeta| order | 6552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×PGL(2,𝔽13) |
| socle | C3×PSL(2,𝔽13) ⋊ C2 |
| derived | PSL(2,𝔽13) ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C3 | PGL(2,𝔽13) |
| commutator, cosocle, hypocenter | PSL(2,𝔽13) | C2×C3 |
| Frattini | C1 | G |
| socle | C3×PSL(2,𝔽13) | C2 |
| LCS | G ▷ PSL(2,𝔽13) | |
| UCS | C1 ◁ C3 | |
70 conjugacy classes of subgroups.
45 conjugacy classes — view the full character table.
| maximal quotient of | C3×#72210881 |
Past the SmallGroups library coverage — no SmallGroups id.