Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×AGL(1,ℤ/8)×C53 ⋊ C4 |
| Sylow | C53 ⋊ #13103 |
646 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 646 conjugacy classes of subgroups — too many to draw. Only its 78 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=f,b^2=dfh,c^2=h,e^2=h,f^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^30,d^b=dg,e^b=eh,f^b=fg,g^b=gh,i^b=i^30,d^c=dh,e^c=eh,f^c=fh,f^d=fh,i^f=i^52320 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1097316);