Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C83×#3407 ⋊ C2 |
| Sylow | C83 ⋊ #12989 |
470 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2656 |
Polycyclic presentation:
2^8,83|a^2=f,b^2=df,f^2=g,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eh,i^a=i^82,d^b=dh,e^b=eh,f^b=fh,d^c=dh,f^c=fh2846 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 86496);