Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Fitting | C43×C53 ⋊ C4 |
| Sylow | C53 ⋊ #13757 |
1598 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 1598 conjugacy classes of subgroups — too many to draw. Only its 440 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=h,c^2=e,d^2=f,b^a=be,c^a=cf,i^a=i^30,i^g=i^52944 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098177);