Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| unambiguous semidirect product | Dic83⋊#338 |
| Sylow | C83 ⋊ C4⋊#338 |
762 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|a^2=f,b^2=g,c^2=e,d^2=h,f^2=h,g^2=h,b^a=bd,c^a=ce,g^a=gh,f^b=fh,i^c=i^821868 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 75374);