Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#430 ⋊ C4 |
| Sylow | C53 ⋊ #11252 |
626 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^8,53|a^2=g,b^2=d,c^2=d,d^2=h,e^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dh,f^a=fh,i^a=i^30,c^b=cf,e^b=eh,f^b=fh,f^c=fh,g^c=gh,i^g=i^52332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1093046);