Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #13095 |
694 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 82 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=h,d^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^23,d^b=dgh,f^b=fgh,g^b=gh,i^b=i^30,i^c=i^52,f^d=fh,i^f=i^52401 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1097287);