Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#20289905 |
| unambiguous semidirect product | D53⋊#1446 |
| Fitting | C23×Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#1446 |
4830 conjugacy classes of subgroups; only the 744 normal subgroups are shown.
This group has 4830 conjugacy classes of subgroups — too many to draw. Only its 744 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3392 |
608 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098344);