Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C83×#1772 ⋊ C2 |
| Sylow | C83 ⋊ C4×#443 |
1046 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|a^2=f,b^2=g,c^2=g,d^2=f,e^2=h,f^2=h,b^a=be,e^a=eh,e^b=eh,i^c=i^82,i^d=i^822408 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 168120);