Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D53⋊M128 |
| Sylow | C53 ⋊ C2×M128 |
134 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 78 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=d,d^2=e,e^2=f,f^2=g,g^2=h,b^a=bh,i^a=i^30,i^c=i^52,i^d=i^52992 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098147);