Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#338 ⋊ C4 |
| Sylow | C53 ⋊ #10813 |
674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=d,d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dh,g^a=gh,i^a=i^23,i^b=i^30,f^c=fh,i^f=i^52,i^g=i^52350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1092217);