Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#13133267 |
| Sylow | C53 ⋊ Q8⋊C32 |
118 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 13568 |
Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=e,d^2=f,f^2=g,g^2=h,b^a=bc,c^a=ce,i^a=i^30,c^b=ce,i^d=i^52632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084479);