Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| unambiguous semidirect product | D53⋊#2971 |
| Sylow | C53 ⋊ C2×#2971 |
2230 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=g,c^2=g,d^2=f,g^2=h,b^a=bf,c^a=ch,d^a=dh,i^a=i^23,c^b=ch,d^c=dh,i^c=i^30,i^e=i^52,i^g=i^52620 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1115150);