Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#504 ⋊ C4 |
| Sylow | C53 ⋊ #12618 |
382 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,e^2=g,g^2=h,b^a=bd,d^a=dh,c^b=cg,e^b=eh,i^b=i^30,f^c=fh,i^f=i^52578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1096044);