Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C53×#418 ⋊ C4 |
| Sylow | C53 ⋊ #10958 |
1230 conjugacy classes of subgroups.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=efh,d^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^23,d^b=dh,e^c=eh,f^c=fh,i^c=i^30,i^f=i^52350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1092647);