Finite Group DatabasebetaFinite Group Databasebeta| order | 19206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D11×C97⋊C9 |
| unambiguous semidirect product | C11⋊(C2×C97⋊C9) |
| unambiguous semidirect product | (D11×C97)⋊C9 |
| derived, Hall | C11×C97 ⋊ C2×C9 |
| Hall | C11×C97⋊C9 ⋊ C2 |
| Hall | D11×C97 ⋊ C9 |
| Sylow | C97 ⋊ C9×D11 |
| Sylow | C11 ⋊ C2×C97⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D11×C97⋊C3 |
| commutator, hypocenter | C11×C97 | C2×C9 |
| Fitting, socle, cosocle | C3×C11×C97 | C2×C3 |
| prime radical | C3×D11×C97 | C3 |
| LCS | G ▷ C11×C97 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9603 |
735 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D11×D97⋊C9, C2×D11×C97⋊C9 |
| maximal normal subgroup of | D11×D97⋊C9, C2×D11×C97⋊C9 |
| maximal quotient of | Dic11×C97⋊C9, C2×D11×C97⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19206, 11);