Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| unambiguous semidirect product | D53⋊#1903 |
| Fitting | C2×AGL(1,ℤ/8)×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#1903 |
1782 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^8,53|a^2=g,b^2=egh,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^23,f^b=fh,i^b=i^30,e^c=eh,f^c=fh,g^c=gh,i^d=i^52,i^g=i^52344 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1105305);