Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Sylow | C79 ⋊ #14678 |
1182 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 371 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 20224 |
Polycyclic presentation:
2^8,79|a^2=e,b^2=h,c^2=g,d^2=ef,b^a=be,c^a=cf,c^b=cg,d^b=def,i^b=i^78,d^c=de,i^c=i^782236 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 100722);