Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #13004 |
560 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=dfgh,d^2=g,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,i^a=i^23,d^b=dg,f^b=fg,g^b=gh,i^b=i^30,i^c=i^52,i^f=i^52332 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1097111);