Finite Group DatabasebetaFinite Group Databasebeta| order | 19026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | D3×C7×C151⋊C3 |
| unambiguous semidirect product | C3⋊(C2×C7×C151⋊C3) |
| unambiguous semidirect product | (D3×C151)⋊(C3×C7) |
| Fitting, socle | C3×C7×C151 ⋊ C2×C3 |
| derived | C3×C151 ⋊ C2×C3×C7 |
| Hall | C3×C7×C151⋊C3 ⋊ C2 |
| Hall | C3×C151⋊C3 ⋊ C2×C7 |
| Hall | C7×C151 ⋊ C3×D3 |
| Sylow | C151 ⋊ C3×D3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D3×C151⋊C3 |
| commutator, cosocle, hypocenter | C3×C151 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C151 | C2×C3 |
| LCS | G ▷ C3×C151 | |
| UCS | C1 ◁ C7 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3171 |
1113 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×D151⋊C3, D3×(C151⋊C3)⋊D7, D3×D7×C151⋊C3, … |
| maximal normal subgroup of | D3×C7×D151⋊C3, D3×(C151⋊C3)⋊D7, D3×D7×C151⋊C3, … |
| maximal quotient of | C7×Dic3×C151⋊C3, C2×D3×C7×C151⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19026, 43);