Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×H(3,ℤ/4)×C83 ⋊ C2 |
| Sylow | C83 ⋊ #23649 |
892 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2656 |
Polycyclic presentation:
2^8,83|a^2=f,c^2=e,e^2=h,b^a=be,c^a=cf,g^a=gh,c^b=cg,e^b=eh,f^b=fh,i^b=i^82,d^c=dh,g^c=gh,i^c=i^821850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 198496);