Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C22⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C2 |
| direct product | C16×C22⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C22×C16)⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | (C7×C16)⋊A4 |
| Fitting, Hall | C22×C7×C16 ⋊ C3 |
| derived | C22×C7 ⋊ C3×C16 |
| Sylow | C22×C16 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ A4×C16 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| 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, 4366);