Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C83×#1297 ⋊ C2 |
| Sylow | C83 ⋊ #8776 |
480 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2656 |
Polycyclic presentation:
2^8,83|a^2=f,c^2=d,e^2=gh,f^2=gh,b^a=bd,c^a=ce,d^a=dg,e^a=eh,f^b=fg,i^b=i^82,e^c=eh,f^c=fg,i^c=i^821601 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 63193);