Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C83×#3091 ⋊ C2 |
| Sylow | C83 ⋊ #61251 |
1842 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|a^2=f,c^2=f,e^2=h,g^2=h,b^a=bf,c^a=cg,d^a=dh,g^a=gh,c^b=ch,d^b=df,g^c=gh,i^d=i^821616 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 1048323);