Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#10620486 |
| derived, Hall | C3×C7 ⋊ C2×C4×C8 |
| Sylow | C7 ⋊ C2×C8×Dic3 |
| Sylow | C3 ⋊ C2×C8×Dic7 |
324 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1344 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 3008);