Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C132 · Schur multiplier (H2) = C13 |
| direct product | C3×C132×D19 |
| Fitting, socle, Hall | C3×C132×C19 ⋊ C2 |
| derived, Sylow | C19 ⋊ C2×C3×C132 |
| Hall | C132×C19 ⋊ C2×C3 |
| Hall | C3×C19 ⋊ C2×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C132 | D19 |
| commutator, cosocle, hypocenter | C19 | C2×C3×C132 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132×C19 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C132 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9633 |
5577 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×D13×D19, C3×D19×C13⋊D13, D3×C132×D19, … |
| maximal normal subgroup of | C3×C13×D13×D19, C3×D19×C13⋊D13, D3×C132×D19, … |
| maximal quotient of | C3×C132×Dic19, C2×C3×C132×D19 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 100);