Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C4×AGL(1,ℤ/8)×C53 ⋊ C2 |
| Sylow | C53 ⋊ #60168 |
2882 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,c^2=g,f^2=h,b^a=bf,e^a=eh,f^a=fh,f^b=fh,d^c=dh,i^d=i^521226 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1033747);