Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| unambiguous semidirect product | #88324⋊C32 |
| Sylow | C53 ⋊ #7331 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13568 |
Polycyclic presentation:
2^8,53|a^2=c,b^2=d,c^2=e,d^2=f,f^2=g,g^2=h,b^a=be,i^a=i^30,i^c=i^52992 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084340);