Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C53×#384 ⋊ C4 |
| Sylow | C53 ⋊ #13830 |
1326 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 352 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=ef,d^2=e,b^a=be,c^a=cf,d^a=def,i^a=i^30,c^b=cef,d^b=de,i^g=i^52440 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098322);