Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C132 · Schur multiplier (H2) = C13 |
| direct product | C132×D57 |
| unambiguous semidirect product | C3⋊(C132×D19) |
| unambiguous semidirect product | C19⋊(D3×C132) |
| Fitting, socle, Hall | C3×C132×C19 ⋊ C2 |
| derived, Hall | C3×C19 ⋊ C2×C132 |
| Hall | C132×C19 ⋊ D3 |
| Hall | C3×C132 ⋊ D19 |
| Sylow | C19 ⋊ D3×C132 |
| Sylow | C3 ⋊ C132×D19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | D57 |
| commutator, cosocle, hypocenter | C3×C19 | C2×C132 |
| Frattini | C1 | G |
| Fitting, socle | C3×C132×C19 | C2 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C132 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9633 |
5070 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C132×D19, C13×D13×D57, C13×D39⋊D19, … |
| maximal normal subgroup of | D3×C132×D19, C13×D13×D57, C13×D39⋊D19, … |
| maximal quotient of | C132×Dic57, C2×C132×D57 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 94);