Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#6399⋊C3 |
| unambiguous semidirect product | (C2×#6399)⋊C3 |
| Fitting | C2×C7×M16 ⋊ C2×C3 |
| Hall | C2×#6399 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#104 |
| Sylow | C7 ⋊ C2×C3×#104 |
340 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 112 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | #72229493, C2×#89970⋊C3, C2×#104×AGL(1,𝔽7), … |
| maximal normal subgroup of | #72229493, C2×#89970⋊C3, C2×#104×AGL(1,𝔽7), … |
| maximal quotient of | D3×#6399⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 1327);