Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #100×D21 |
| Fitting | C3×C7×#100 ⋊ C2 |
| Hall | C3×C7 ⋊ C2×#100 |
| Sylow | C7 ⋊ D3×#100 |
| Sylow | C3 ⋊ D7×#100 |
372 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 168 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D7×#100, D21×#453, #72244315, … |
| maximal normal subgroup of | D3×D7×#100, D21×#453, #72244315, … |
| maximal quotient of | #72246817 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5670);