Finite Group DatabasebetaFinite Group Databasebeta| order | 19166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C37 |
| unambiguous semidirect product | C7⋊(C37⋊D37) |
| unambiguous semidirect product | C37⋊D259 |
| Fitting, socle, derived, Hall | C7×C372 ⋊ C2 |
| Sylow | C372 ⋊ D7 |
| Sylow | C7 ⋊ C37⋊D37 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C372 | C2 |
| LCS | G ▷ C7×C372 | |
| UCS | C1 | |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9583 |
Polycyclic presentation:
2,7,37^2|b^a=b^6,c^a=c^36,d^a=d^364793 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D37×D259, D7×C37⋊D37, C2×C7⋊(C37⋊D37) |
| maximal normal subgroup of | D37×D259, D7×C37⋊D37, C2×C7⋊(C37⋊D37) |
| maximal quotient of | C7⋊#19129955, C2×C7⋊(C37⋊D37) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19166, 6);