Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C4×D8×C53 ⋊ C4 |
| Sylow | C53 ⋊ #20508 |
1206 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=g,d^2=fh,e^2=h,b^a=be,c^a=ch,d^a=dh,e^a=eh,i^a=i^23,e^b=eh,d^c=dh,i^d=i^30,i^f=i^52452 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1104069);