Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C83 ⋊ #11827 |
418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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,b^2=h,c^2=gh,d^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fh,i^a=i^82,c^b=ch,d^b=dg,e^b=efg,i^b=i^82,e^d=eh1340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 80365);