Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C43 · Schur multiplier (H2) = C27×C43 |
| direct product | C22×C42×Dic89 |
| derived, Sylow | C89 ⋊ C22×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C42 | D89 |
| commutator, hypocenter | C89 | C22×C43 |
| Frattini | C23 | C24×D89 |
| Fitting | C23×C42×C89 | C2 |
| socle, prime radical | C25×C89 | C23 |
| cosocle | C23×C89 | C25 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C23×C42 | |
8094 conjugacy classes of subgroups; only the 5547 normal subgroups are shown.
This group has 8094 conjugacy classes of subgroups — too many to draw. Only its 5547 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 22784 |
5888 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 327733);