Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C214 |
| unambiguous semidirect product | D53⋊#3573 |
| Sylow | C53 ⋊ C2×#3573 |
10858 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,g^2=h,i^a=i^30,e^b=eh,d^c=dh,i^f=i^52,i^g=i^52578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1116303);