Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8 |
| unambiguous semidirect product | D53⋊#1455 |
| Sylow | C53 ⋊ C2×#1455 |
994 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,e^2=g,f^2=h,c^a=cg,i^a=i^30,c^b=ch,i^d=i^52,i^e=i^52632 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1099370);