Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C83×#3195 ⋊ C2 |
| Sylow | C83 ⋊ #12115 |
422 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 59 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|b^2=h,d^2=fh,f^2=h,b^a=bd,c^a=ce,d^a=df,f^a=fh,g^a=gh,i^a=i^82,d^b=df,e^b=egh,f^b=fh,d^c=dg,e^d=eh1091 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 81738);