Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C83×#1787 ⋊ C2 |
| Sylow | C83 ⋊ #9471 |
716 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|a^2=f,b^2=df,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eh,c^b=cg,e^b=eh,d^c=dh,f^c=fh,i^c=i^821595 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 67344);