Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D53⋊#2179 |
| Fitting | C53×#508 ⋊ C4 |
| Sylow | C53 ⋊ C2×#2179 |
654 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=f,c^2=f,e^2=gh,f^2=h,g^2=h,b^a=be,c^a=ch,e^a=eg,g^a=gh,i^a=i^23,e^b=eg,g^b=gh,i^c=i^30,i^d=i^52,i^f=i^52350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1113860);