Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #12066 |
214 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 13568 |
Polycyclic presentation:
2^8,53|a^2=e,b^2=h,c^2=ef,d^2=f,e^2=g,f^2=h,b^a=bd,c^a=cf,d^a=df,f^a=fh,i^a=i^23,d^b=dfh,e^b=eh,f^b=fh,d^c=dh,i^c=i^30,i^e=i^52332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1095538);