Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4 |
| unambiguous semidirect product | D53⋊#2920 |
| Sylow | C53 ⋊ C2×#2920 |
2806 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,c^2=f,g^2=h,b^a=bf,d^a=dh,i^a=i^30,i^e=i^52,i^g=i^52944 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114825);