Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×#10621615 |
| Fitting, Hall | C2×C7×H(5,𝔽2) ⋊ C3 |
| Sylow | C2×H(5,𝔽2) ⋊ ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C2×#994 |
416 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 336 |
106 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 11604);