Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C79×#1726 ⋊ C2 |
| Sylow | C79 ⋊ #21670 |
656 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 227 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|a^2=g,b^2=ef,c^2=e,d^2=g,g^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^78,c^b=ch3184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 177847);