Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C22⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C27 |
| direct product | C24×C22⋊ΓL(1,𝔽8) |
| Fitting, socle, Hall | C26×C7 ⋊ C3 |
| derived | C22×C7 ⋊ C24×C3 |
| Sylow | C26 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C24×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | C22⋊ΓL(1,𝔽8) |
| commutator, cosocle, hypocenter | C22×C7 | C24×C3 |
| Frattini | C1 | G |
| Fitting, socle | C26×C7 | C3 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C24 | |
2330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11712);