Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| unambiguous semidirect product | D53⋊#2123 |
| Fitting | C53×#536 ⋊ C4 |
| Sylow | C53 ⋊ C2×#2123 |
1214 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=h,b^a=be,e^a=eg,g^a=gh,i^a=i^30,c^b=ch,f^b=fg,i^d=i^52,f^e=fh,i^f=i^52332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1113472);