Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
No aliases for this group.
| Sylow | C79 ⋊ #20370 |
908 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 407 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2528 |
Polycyclic presentation:
2^8,79|a^2=f,b^2=g,c^2=e,e^2=h,b^a=be,g^a=gh,i^a=i^78,f^b=fh,i^b=i^78,d^c=dh,i^c=i^781798 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 167076);