Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C83×#1326 ⋊ C2 |
| Sylow | C83 ⋊ #11578 |
426 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 71 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=e,b^2=f,c^2=g,e^2=g,b^a=bd,d^a=df,f^a=fh,c^b=cgh,d^b=dh,e^b=ef,i^c=i^82,e^d=eh1103 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 79252);