Finite Group DatabasebetaFinite Group Databasebeta| order | 1344 |
| isoclinism | isoclinic class of #66632 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#66632 |
| Fitting | C3×C4×C7×D4 ⋊ C2 |
| Hall | C3×C7 ⋊ C4×D8 |
| Sylow | C7 ⋊ C4×#213 |
| Sylow | C3 ⋊ C4×#1141 |
268 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 672 |
228 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1344, 5939);