Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C8 |
| direct product | C2×#23761702 |
| Fitting | C2×C82×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×#1455 |
994 conjugacy classes of subgroups; only the 475 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 475 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 10112 |
5104 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 135273);