Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
| unambiguous semidirect product | D53⋊#1412 |
| Fitting | C53×#490 ⋊ C4 |
| Sylow | C53 ⋊ C2×#1412 |
390 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=g,d^2=gh,f^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^30,d^b=dg,e^b=efg,f^b=fh,i^c=i^52,e^d=egh,f^e=fh,i^e=i^52236 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1097941);