Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C53 ⋊ #17961 |
598 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6784 |
Polycyclic presentation:
2^8,53|a^2=f,b^2=g,c^2=f,e^2=g,f^2=h,b^a=be,c^a=cg,d^a=dh,e^a=eg,i^a=i^30,d^b=dh,e^b=eg,i^c=i^30,i^d=i^52,i^f=i^52350 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1102488);