Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#563 ⋊ C4 |
| Sylow | C53 ⋊ #12780 |
756 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 756 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) = 1696 |
Polycyclic presentation:
2^8,53|a^2=f,c^2=h,d^2=h,e^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^30,d^b=dh,e^b=eg,f^b=fgh,d^c=dgh,e^c=eh,f^c=fh,e^d=eh,f^d=fh,i^f=i^52281 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1096590);