Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C132 · Schur multiplier (H2) = C13 |
| direct product | C132×D19⋊C3 |
| unambiguous semidirect product | D19⋊(C3×C132) |
| unambiguous semidirect product | (C19⋊C3)⋊(C2×C132) |
| Fitting, socle, Hall | C132×C19 ⋊ C2×C3 |
| derived, Sylow | C19 ⋊ C2×C3×C132 |
| Hall | C132×C19⋊C3 ⋊ C2 |
| Hall | C132×D19 ⋊ C3 |
| Hall | C19⋊C3 ⋊ C2×C132 |
| Hall | D19 ⋊ C3×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | D19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C2×C3×C132 |
| Frattini | C1 | G |
| Fitting, socle | C132×C19 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C132 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3211 |
1521 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D13×D19⋊C3, D19⋊C3×C13⋊D13, C2×C132×D19⋊C3 |
| maximal normal subgroup of | C13×D13×D19⋊C3, D19⋊C3×C13⋊D13, C2×C132×D19⋊C3 |
| maximal quotient of | C132×(C19⋊C3)⋊C4, C2×C132×D19⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 26);