Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C53×#453 ⋊ C2 |
| Sylow | C53 ⋊ #61110 |
2684 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^8,53|a^2=h,f^2=h,g^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,g^a=gh,i^a=i^52,d^b=df,e^b=eh,f^b=fh,g^c=gh,i^c=i^52,f^d=fh,i^d=i^52884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1045877);