Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#2216 ⋊ C2 |
| Sylow | C79 ⋊ #33828 |
488 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10112 |
Polycyclic presentation:
2^8,79|b^2=h,d^2=eh,f^2=gh,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fg,g^a=gh,i^a=i^78,c^b=ce,d^b=dh,f^c=fg,g^c=gh,i^c=i^78,i^d=i^781522 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 326008);