Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #7311 |
590 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 848 |
Polycyclic presentation:
2^8,53|a^2=d,b^2=e,d^2=h,b^a=bc,c^a=cf,e^a=eg,f^a=fh,g^a=gh,i^a=i^30,c^b=cg,d^b=df,f^b=fh,d^c=dh,e^d=eh,i^d=i^52392 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084286);