Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of SL(2,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7×C8 · Schur multiplier (H2) = C1 |
| direct product | C7×#504⋊C3 |
| unambiguous semidirect product | #504⋊(C3×C7) |
| Fitting, Hall | C7×#504 ⋊ C3 |
| Sylow | #504 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C16 | A4 |
| commutator, hypocenter | Q8 | C3×C7×C8 |
| Frattini | C8 | C2×C7×A4 |
| Fitting | C7×#504 | C3 |
| socle | C2×C7 | C8×A4 |
| prime radical | C7×#41⋊C3 | C4 |
| cosocle | #131 | C2×C3×C7 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C7×C16 | |
58 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
392 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4347);