Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| unambiguous semidirect product | D53⋊#1840 |
| Sylow | C53 ⋊ C2×#1840 |
894 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 272 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=g,b^2=ef,c^2=e,g^2=h,b^a=be,c^a=cf,i^a=i^30,c^b=ch,i^d=i^52,i^g=i^52608 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1104837);