Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of Dic14 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C8 · Schur multiplier (H2) = C22 |
| direct product | C7×(C2×D7)⋊C8 |
| unambiguous semidirect product | (C2×D7)⋊(C7×C8) |
| Fitting | C2×C72×C8 ⋊ C2 |
| Sylow | C72 ⋊ C22⋊C8 |
133 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 133 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 224 |
476 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 262);