Finite Group DatabasebetaFinite Group Databasebeta| order | 22022 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D847 |
| unambiguous semidirect product | C7⋊(C13×D121) |
| unambiguous semidirect product | C121⋊(C13×D7) |
| Fitting, Hall | C7×C13×C121 ⋊ C2 |
| derived, Hall | C7×C121 ⋊ C2×C13 |
| Hall | C13×C121 ⋊ D7 |
| Sylow | C121 ⋊ C13×D7 |
| Hall | C7×C13 ⋊ D121 |
| Sylow | C7 ⋊ C13×D121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D847 |
| commutator, cosocle, hypocenter | C7×C121 | C2×C13 |
| Frattini | C11 | C13×D77 |
| Fitting | C7×C13×C121 | C2 |
| socle | C7×C11×C13 | D11 |
| LCS | G ▷ C7×C121 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11011 |
5525 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22022, 7);