Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D53⋊#2169 |
| Sylow | C53 ⋊ C2×#2169 |
742 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=f,c^2=f,f^2=g,g^2=h,b^a=be,c^a=ch,i^a=i^23,c^b=ch,i^c=i^30,i^d=i^52,i^f=i^52632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1113778);