Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C83×#1764 ⋊ C2 |
| Sylow | C83 ⋊ #22468 |
1316 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|a^2=g,c^2=h,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dh,e^a=eh,i^a=i^82,d^b=de,e^b=eh,i^b=i^82,f^c=fh,g^c=gh,e^d=eh,i^d=i^822354 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 185615);