Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C23×#13133211 |
| Fitting | C23×C42×C53 ⋊ C2 |
| Sylow | C53 ⋊ C23×#126 |
9486 conjugacy classes of subgroups; only the 3915 normal subgroups are shown.
This group has 9486 conjugacy classes of subgroups — too many to draw. Only its 3915 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6784 |
3440 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1076239);