Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×C53×#575 ⋊ C2 |
| Sylow | C53 ⋊ #60387 |
4764 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|e^2=h,f^2=h,b^a=bf,c^a=cg,d^a=dh,f^a=fh,f^b=fh,g^b=gh,f^c=fh,i^c=i^521202 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1036236);