Finite Group DatabasebetaFinite Group Databasebeta| order | 20746 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D253 |
| unambiguous semidirect product | C11⋊(C41×D23) |
| unambiguous semidirect product | C23⋊(D11×C41) |
| Fitting, socle, Hall | C11×C23×C41 ⋊ C2 |
| derived, Hall | C11×C23 ⋊ C2×C41 |
| Hall | C23×C41 ⋊ D11 |
| Hall | C11×C41 ⋊ D23 |
| Sylow | C23 ⋊ D11×C41 |
| Sylow | C11 ⋊ C41×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D253 |
| commutator, cosocle, hypocenter | C11×C23 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C11×C23×C41 | C2 |
| LCS | G ▷ C11×C23 | |
| UCS | C1 ◁ C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10373 |
5248 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20746, 8);