Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C8×M16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #9550 |
378 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|a^2=f,b^2=dfg,c^2=d,d^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^82,e^c=eg3344 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 67804);