Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D53⋊#1418 |
| Fitting | C53×#508 ⋊ C4 |
| Sylow | C53 ⋊ C2×#1418 |
302 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=e,d^2=fgh,f^2=gh,g^2=h,b^a=bd,d^a=df,f^a=fg,g^a=gh,i^a=i^30,d^b=dfh,e^b=eh,f^b=fg,g^b=gh,i^c=i^52,i^e=i^52338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098044);