Finite Group DatabasebetaFinite Group Databasebeta| order | 22188 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C1849 · Schur multiplier (H2) = C2 |
| direct product | A4×C1849 |
| unambiguous semidirect product | C22⋊(C3×C1849) |
| Fitting, Hall | C22×C1849 ⋊ C3 |
| derived, Sylow | C22 ⋊ C3×C1849 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1849 | A4 |
| commutator, hypocenter | C22 | C3×C1849 |
| Frattini | C43 | A4×C43 |
| Fitting | C22×C1849 | C3 |
| socle, cosocle | C22×C43 | C3×C43 |
| prime radical | A4×C43 | C43 |
| LCS | G ▷ C22 | |
| UCS | C1 ◁ C1849 | |
15 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7396 |
7396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22188, 11);