Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C26 |
| direct product | C2×#6493⋊C3 |
| unambiguous semidirect product | (C2×#6493)⋊C3 |
| Fitting | C23×C4×C7 ⋊ C2×C3 |
| Hall | C2×#6493 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#121 |
| Sylow | C7 ⋊ C2×C3×#121 |
852 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 240 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
116 conjugacy classes — view the full character table.
| maximal subgroup of | #72259933, C2×#121×AGL(1,𝔽7) |
| maximal normal subgroup of | #72259933, C2×#121×AGL(1,𝔽7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6813);