Finite Group DatabasebetaFinite Group Databasebeta| order | 20229 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C613⋊C3 |
| unambiguous semidirect product | C613⋊(C3×C11) |
| unambiguous semidirect product | (C11×C613)⋊C3 |
| Fitting, socle, Hall | C11×C613 ⋊ C3 |
| derived, Sylow | C613 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C613⋊C3 |
| commutator, cosocle, hypocenter | C613 | C3×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C613 | C3 |
| LCS | G ▷ C613 | |
| UCS | C1 ◁ C11 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6743 |
2277 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20229, 1);