Finite Group DatabasebetaFinite Group Databasebeta| order | 19090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D1909 |
| unambiguous semidirect product | C23⋊(C5×D83) |
| unambiguous semidirect product | C83⋊(C5×D23) |
| Fitting, socle, Hall | C5×C23×C83 ⋊ C2 |
| derived, Hall | C23×C83 ⋊ C2×C5 |
| Hall | C5×C83 ⋊ D23 |
| Hall | C5×C23 ⋊ D83 |
| Sylow | C83 ⋊ C5×D23 |
| Sylow | C23 ⋊ C5×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D1909 |
| commutator, cosocle, hypocenter | C23×C83 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C23×C83 | C2 |
| LCS | G ▷ C23×C83 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9545 |
4780 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D23×D83, D5×D1909, D115⋊D83, … |
| maximal normal subgroup of | C5×D23×D83, D5×D1909, D115⋊D83, … |
| maximal quotient of | C5×Dic1909, C2×C5×D1909 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19090, 4);