Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C22⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C42×C22⋊ΓL(1,𝔽8) |
| Fitting, Hall | C22×C42×C7 ⋊ C3 |
| derived | C22×C7 ⋊ C3×C42 |
| Sylow | C22×C42 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C42×A4 |
266 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, 10058);