Finite Group DatabasebetaFinite Group Databasebeta| order | 19190 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D19×C101⋊C5 |
| unambiguous semidirect product | C19⋊(C2×C101⋊C5) |
| unambiguous semidirect product | (D19×C101)⋊C5 |
| Fitting, socle, derived, Hall | C19×C101 ⋊ C2×C5 |
| Hall | C19×C101⋊C5 ⋊ C2 |
| Hall | D19×C101 ⋊ C5 |
| Sylow | C101 ⋊ C5×D19 |
| Sylow | C19 ⋊ C2×C101⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C101 | C2×C5 |
| LCS | G ▷ C19×C101 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1919 |
275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D19×D101⋊C5, C2×D19×C101⋊C5 |
| maximal normal subgroup of | D19×D101⋊C5, C2×D19×C101⋊C5 |
| maximal quotient of | Dic19×C101⋊C5, C2×D19×C101⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19190, 11);