Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C4×#137×C53 ⋊ C2 |
| Sylow | C53 ⋊ #61097 |
2654 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6784 |
Polycyclic presentation:
2^8,53|b^2=h,d^2=h,f^2=h,b^a=bf,c^a=cg,e^a=eh,f^a=fh,i^a=i^52,d^b=df,e^b=eh,f^b=fh,e^c=eh,i^c=i^52,f^d=fh1199 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1045739);