Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D53⋊(Q8⋊C16) |
| Sylow | C53 ⋊ C2×Q8⋊C16 |
382 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6784 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,d^2=f,e^2=g,g^2=h,b^a=bd,d^a=df,i^a=i^30,d^b=df,i^c=i^52,i^e=i^52632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1094000);