Finite Group DatabasebetaFinite Group Databasebeta| order | 22126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D851 |
| unambiguous semidirect product | C23⋊(C13×D37) |
| unambiguous semidirect product | C37⋊(C13×D23) |
| Fitting, socle, Hall | C13×C23×C37 ⋊ C2 |
| derived, Hall | C23×C37 ⋊ C2×C13 |
| Hall | C13×C37 ⋊ D23 |
| Hall | C13×C23 ⋊ D37 |
| Sylow | C37 ⋊ C13×D23 |
| Sylow | C23 ⋊ C13×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D851 |
| commutator, cosocle, hypocenter | C23×C37 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C23×C37 | C2 |
| LCS | G ▷ C23×C37 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11063 |
5551 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22126, 4);