Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C79×#2198 ⋊ C2 |
| Sylow | C79 ⋊ #33546 |
1236 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1264 |
Polycyclic presentation:
2^8,79|d^2=h,b^a=be,c^a=cf,g^a=gh,f^b=fgh,i^b=i^78,e^c=eg,i^c=i^78,i^d=i^78,f^e=fh820 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 323590);