Finite Group DatabasebetaFinite Group Databasebeta| order | 19026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1359 |
| unambiguous semidirect product | C9⋊(C7×D151) |
| unambiguous semidirect product | C151⋊(C7×D9) |
| Fitting, Hall | C7×C9×C151 ⋊ C2 |
| derived, Hall | C9×C151 ⋊ C2×C7 |
| Hall | C7×C151 ⋊ D9 |
| Sylow | C151 ⋊ C7×D9 |
| Hall | C7×C9 ⋊ D151 |
| Sylow | C9 ⋊ C7×D151 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1359 |
| commutator, cosocle, hypocenter | C9×C151 | C2×C7 |
| Frattini | C3 | C7×D453 |
| Fitting | C7×C9×C151 | C2 |
| socle | C3×C7×C151 | D3 |
| LCS | G ▷ C9×C151 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9513 |
4767 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D9×D151, D7×D1359, D63⋊D151, … |
| maximal normal subgroup of | C7×D9×D151, D7×D1359, D63⋊D151, … |
| maximal quotient of | C7×Dic1359, C2×C7×D1359 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19026, 10);