Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C53×#557 ⋊ C4 |
| Sylow | C53 ⋊ #8433 |
672 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=h,c^2=g,d^2=h,e^2=g,f^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^30,d^b=dh,f^b=fgh,i^b=i^52,e^c=eg,f^c=fg,i^f=i^52368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1088049);