Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C82×C53 ⋊ C4 |
| Sylow | C53 ⋊ #8803 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=de,c^2=d,d^2=gh,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,i^a=i^30,f^b=fh,f^c=fgh,i^f=i^52872 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1089045);