Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#349 ⋊ C4 |
| Sylow | C53 ⋊ #7191 |
342 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 68 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=g,g^2=h,b^a=bc,c^a=cf,f^a=fh,d^b=df,i^b=i^30,d^c=dh,i^e=i^52338 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1083905);