Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×M32×C83 ⋊ C2 |
| Sylow | C83 ⋊ #33443 |
648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2656 |
Polycyclic presentation:
2^8,83|a^2=f,c^2=f,e^2=h,f^2=g,g^2=h,b^a=be,d^a=dh,e^a=eh,i^a=i^82,e^b=eh,i^b=i^82,d^c=dh3368 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 322824);