Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C53×2−1+6 ⋊ C2 |
| Sylow | C53 ⋊ #60400 |
4732 conjugacy classes of subgroups; only the 807 normal subgroups are shown.
This group has 4732 conjugacy classes of subgroups — too many to draw. Only its 807 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|d^2=h,e^2=h,b^a=bf,c^a=cg,i^a=i^52,g^b=gh,f^c=fh,e^d=eh1748 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1036325);