Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Fitting | C53×#343 ⋊ C4 |
| Sylow | C53 ⋊ #10711 |
842 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=g,g^2=h,b^a=bd,d^a=dh,i^a=i^23,e^b=eh,i^c=i^30,i^e=i^52,i^g=i^52374 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1091898);