Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×D16×C83 ⋊ C2 |
| Sylow | C83 ⋊ #13304 |
670 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10624 |
Polycyclic presentation:
2^8,83|d^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,c^b=cf,d^b=dg,g^b=gh,i^c=i^821856 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 88262);