Finite Group DatabasebetaFinite Group Databasebeta| order | 19190 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1919 |
| unambiguous semidirect product | C19⋊(C5×D101) |
| Fitting, socle, Hall | C5×C19×C101 ⋊ C2 |
| derived, Hall | C19×C101 ⋊ C2×C5 |
| Hall | C5×C101 ⋊ D19 |
| Sylow | C101 ⋊ C5×D19 |
| Hall | C5×C19 ⋊ D101 |
| Sylow | C19 ⋊ C5×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1919 |
| commutator, cosocle, hypocenter | C19×C101 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C19×C101 | C2 |
| LCS | G ▷ C19×C101 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9595 |
4805 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D19×D101, D5×D1919, D95⋊D101, … |
| maximal normal subgroup of | C5×D19×D101, D5×D1919, D95⋊D101, … |
| maximal quotient of | C5×Dic1919, C2×C5×D1919 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19190, 5);