Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
| unambiguous semidirect product | D53⋊#1747 |
| Fitting | C53×#405 ⋊ C4 |
| Sylow | C53 ⋊ C2×#1747 |
930 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=e,e^2=h,b^a=be,g^a=gh,i^a=i^30,f^b=fh,i^d=i^52,i^f=i^52608 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1103511);