Finite Group DatabasebetaFinite Group Databasebeta| order | 19206 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×D99 |
| unambiguous semidirect product | C9⋊(D11×C97) |
| unambiguous semidirect product | C11⋊(D9×C97) |
| Fitting, Hall | C9×C11×C97 ⋊ C2 |
| derived, Hall | C9×C11 ⋊ C2×C97 |
| Hall | C11×C97 ⋊ D9 |
| Hall | C9×C97 ⋊ D11 |
| Sylow | C11 ⋊ D9×C97 |
| Sylow | C9 ⋊ D11×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | D99 |
| commutator, cosocle, hypocenter | C9×C11 | C2×C97 |
| Frattini | C3 | D33×C97 |
| Fitting | C9×C11×C97 | C2 |
| socle | C3×C11×C97 | D3 |
| LCS | G ▷ C9×C11 | |
| UCS | C1 ◁ C97 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9603 |
4947 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D97×D99, D9×D11×C97, D99⋊D97, … |
| maximal normal subgroup of | D97×D99, D9×D11×C97, D99⋊D97, … |
| maximal quotient of | C97×Dic99, C2×C97×D99 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19206, 8);