Finite Group DatabasebetaFinite Group Databasebeta| order | 19166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D259 |
| unambiguous semidirect product | C7⋊(C37×D37) |
| unambiguous semidirect product | C37⋊(D7×C37) |
| Fitting, socle, Hall | C7×C372 ⋊ C2 |
| derived | C7×C37 ⋊ C2×C37 |
| Sylow | C372 ⋊ D7 |
| Sylow | C7 ⋊ C37×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D259 |
| commutator, cosocle, hypocenter | C7×C37 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C7×C372 | C2 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C37 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 518 |
4847 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C37×D37, D37×D259, D259⋊D37, … |
| maximal normal subgroup of | D7×C37×D37, D37×D259, D259⋊D37, … |
| maximal quotient of | C37×Dic259, C2×C37×D259 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19166, 7);