Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C83×#1420 ⋊ C2 |
| Sylow | C83 ⋊ #13657 |
182 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5312 |
Polycyclic presentation:
2^8,83|a^2=e,c^2=eg,d^2=fgh,f^2=gh,g^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fg,g^a=gh,i^a=i^82,d^b=dfh,e^b=eh,f^b=fg,g^b=gh,i^b=i^82,d^c=dh,i^c=i^821100 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 90189);