Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #12060 |
204 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 86 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=f,c^2=e,d^2=f,e^2=g,g^2=h,b^a=bd,c^a=cfh,d^a=df,i^a=i^30,d^b=df,i^c=i^30,i^e=i^52440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1095511);