Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C53×#391 ⋊ C4 |
| Sylow | C53 ⋊ #9466 |
726 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=dfh,c^2=gh,d^2=gh,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=egh,i^a=i^30,d^b=dh,e^b=egh,f^b=fh,i^b=i^30,d^c=dgh,f^c=fgh,i^f=i^52401 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1090718);