Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | #102×AGL(1,𝔽7) |
| unambiguous semidirect product | D7⋊(C3×#102) |
| unambiguous semidirect product | (D7×#102)⋊C3 |
| Fitting | C7×#102 ⋊ C2×C3 |
| Hall | D7×#102 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#102 |
| Sylow | C7 ⋊ C2×C3×#102 |
404 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 112 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 957);