Finite Group DatabasebetaFinite Group Databasebeta| order | 19206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D97⋊C9 |
| unambiguous semidirect product | D97⋊(C9×C11) |
| unambiguous semidirect product | (C97⋊C9)⋊(C2×C11) |
| unambiguous semidirect product | (C11×D97)⋊C9 |
| derived, Sylow | C97 ⋊ C2×C9×C11 |
| Hall | C11×C97⋊C9 ⋊ C2 |
| Hall | C11×D97 ⋊ C9 |
| Hall | C11×C97 ⋊ C2×C9 |
| Hall | C97⋊C9 ⋊ C2×C11 |
| Hall | D97 ⋊ C9×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C11 | D97⋊C3 |
| commutator, hypocenter | C97 | C2×C9×C11 |
| Frattini | C3 | C11×D97⋊C3 |
| Fitting, socle | C3×C11×C97 | C2×C3 |
| prime radical | C3×C11×D97 | C3 |
| cosocle | C3×C97 | C2×C3×C11 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C3×C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9603 |
726 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×#87604⋊C9, C11⋊(#87604⋊C9), D11×D97⋊C9, … |
| maximal normal subgroup of | C11×#87604⋊C9, C11⋊(#87604⋊C9), D11×D97⋊C9, … |
| maximal quotient of | C11×Dic97⋊C9, C2×C11×D97⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19206, 10);