Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C53×H(3,ℤ/4) ⋊ C4 |
| Sylow | C53 ⋊ #10699 |
842 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=g,d^2=h,g^2=h,b^a=bd,f^a=fh,e^b=eh,i^c=i^30,i^g=i^52374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1091846);