Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #7049 |
304 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 13568 |
Polycyclic presentation:
2^8,53|a^2=d,b^2=e,c^2=fh,d^2=fgh,e^2=h,b^a=bc,c^a=cf,e^a=efgh,i^a=i^30,c^b=cg,d^b=dh,i^d=i^52572 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1083558);