Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#461 ⋊ C4 |
| Sylow | C53 ⋊ #8985 |
680 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,d^2=g,e^2=h,f^2=g,b^a=bd,c^a=ce,i^a=i^23,d^b=dg,e^b=eh,f^b=fg,i^b=i^30,d^c=dh,e^c=eh,f^c=fh,i^f=i^52299 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1089516);