Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×#13133282 |
| Fitting | C23×Q8×C53 ⋊ C4 |
| Sylow | C53 ⋊ C23×#104 |
5758 conjugacy classes of subgroups; only the 1208 normal subgroups are shown.
This group has 5758 conjugacy classes of subgroups — too many to draw. Only its 1208 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3392 |
632 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114756);