Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#509×C83 ⋊ C2 |
| Sylow | C83 ⋊ #13341 |
594 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 101 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|d^2=gh,e^2=g,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=egh,f^a=fh,g^a=gh,c^b=cf,d^b=dg,e^b=eg,f^b=fh,g^b=gh,d^c=dgh,e^c=egh,f^c=fh,g^c=gh,i^c=i^821346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 88495);