Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×#6467⋊C3 |
| unambiguous semidirect product | (C2×#6467)⋊C3 |
| Fitting | C22×C7×C8 ⋊ C2×C3 |
| Hall | C2×#6467 ⋊ C3 |
| Hall | ΓL(1,𝔽8) ⋊ C2×#135 |
| Sylow | C7 ⋊ C2×C3×#135 |
532 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 192 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.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 6764);