Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#19151384 |
| Fitting | C22×#99×C89 ⋊ C2 |
| Sylow | C89 ⋊ C22×AΣL(1,𝔽16) |
2774 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 2774 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2848 |
1988 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 322278);