Finite Group DatabasebetaFinite Group Databasebeta| order | 19166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C37 |
| direct product | C7×C37⋊D37 |
| unambiguous semidirect product | C37⋊(C7×D37) |
| Fitting, socle, Hall | C7×C372 ⋊ C2 |
| derived, Sylow | C372 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C37⋊D37 |
| commutator, cosocle, hypocenter | C372 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C372 | C2 |
| LCS | G ▷ C372 | |
| UCS | C1 ◁ C7 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9583 |
4802 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D372, C7×#19129958, C7×#19129959, … |
| maximal normal subgroup of | C7×D372, C7×#19129958, C7×#19129959, … |
| maximal quotient of | C7×#19129955, C2×C7×C37⋊D37 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19166, 9);