Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of C7⋊(C42⋊C3) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C4 |
| direct product | C4×C7⋊(C42⋊C3) |
| unambiguous semidirect product | (C4×C7)⋊(C42⋊C3) |
| Fitting, Hall | C43×C7 ⋊ C3 |
| derived | C42×C7 ⋊ C3×C4 |
| Sylow | C43 ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C4×C42⋊C3 |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 84 |
160 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 4348);