Finite Group DatabasebetaFinite Group Databasebeta| order | 19162 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D871 |
| unambiguous semidirect product | C13⋊(C11×D67) |
| Fitting, socle, Hall | C11×C13×C67 ⋊ C2 |
| derived, Hall | C13×C67 ⋊ C2×C11 |
| Hall | C11×C67 ⋊ D13 |
| Hall | C11×C13 ⋊ D67 |
| Sylow | C67 ⋊ C11×D13 |
| Sylow | C13 ⋊ C11×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D871 |
| commutator, cosocle, hypocenter | C13×C67 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C11×C13×C67 | C2 |
| LCS | G ▷ C13×C67 | |
| UCS | C1 ◁ C11 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9581 |
4807 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C11×D13×D67, D11×D871, D143⋊D67, … |
| maximal normal subgroup of | C11×D13×D67, D11×D871, D143⋊D67, … |
| maximal quotient of | C11×Dic871, C2×C11×D871 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19162, 5);