Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Fitting | C53×#376 ⋊ C4 |
| Sylow | C53 ⋊ #13797 |
1438 conjugacy classes of subgroups; only the 400 normal subgroups are shown.
This group has 1438 conjugacy classes of subgroups — too many to draw. Only its 400 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=g,b^2=f,c^2=h,d^2=e,b^a=be,c^a=cf,d^a=de,i^a=i^30,c^b=ce,i^g=i^52608 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098258);