Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#518 ⋊ C4 |
| Sylow | C53 ⋊ #20710 |
1276 conjugacy classes of subgroups; only the 260 normal subgroups are shown.
This group has 1276 conjugacy classes of subgroups — too many to draw. Only its 260 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|a^2=g,c^2=e,d^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^30,g^b=gh,f^c=fh,i^d=i^52,i^g=i^52500 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1104678);