Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| unambiguous semidirect product | D53⋊#1876 |
| Fitting | C2×#135×C53 ⋊ C4 |
| Sylow | C53 ⋊ C2×#1876 |
1754 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,b^2=eg,e^2=h,f^2=h,b^a=be,c^a=cf,i^a=i^23,e^b=eh,f^b=fh,g^b=gh,i^b=i^30,e^c=eh,f^c=fh,g^c=gh,i^d=i^52,i^g=i^52440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1105166);