Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C79×#3529 ⋊ C2 |
| Sylow | C79 ⋊ #33564 |
1112 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 167 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|d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fh,g^a=gh,i^a=i^78,e^b=eh,f^b=fgh,e^c=eg,f^c=fh,f^e=fh1516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 323732);