Finite Group DatabasebetaFinite Group Databasebeta| order | 22784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C26 |
| direct product | C22×C32×D89 |
| Fitting | C22×C32×C89 ⋊ C2 |
| derived, Sylow | C89 ⋊ C23×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | D89 |
| commutator, hypocenter | C89 | C23×C32 |
| Frattini | C16 | C23×D89 |
| Fitting | C22×C32×C89 | C2 |
| socle | C23×C89 | C2×C16 |
| prime radical | C23×D89 | C16 |
| cosocle | C16×C89 | C24 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C22×C32 | |
542 conjugacy classes of subgroups; only the 331 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 331 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11392 |
5888 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22784, 327670);