Finite Group DatabasebetaFinite Group Databasebeta| order | 21568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×#13062438 |
| unambiguous semidirect product | D337⋊(C4×D4) |
| Fitting | C2×D4×C337 ⋊ C4 |
| Sylow | C337 ⋊ C2×C4×D4 |
426 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2696 |
880 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21568, 1613);