Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C83×#1286 ⋊ C2 |
| Sylow | C83 ⋊ #9299 |
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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=dfh,d^2=gh,e^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eg,i^a=i^82,d^b=dh,e^b=egh,f^b=fh,d^c=dgh,e^c=eh,f^c=fgh,i^c=i^821352 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 66296);