Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C79×#1822 ⋊ C2 |
| Sylow | C79 ⋊ #23953 |
1166 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 5056 |
Polycyclic presentation:
2^8,79|b^2=e,c^2=h,d^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,g^a=gh,i^a=i^78,c^b=cg,f^b=fh,d^c=dh,f^c=fh,i^c=i^781288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 201639);