Finite Group DatabasebetaFinite Group Databasebeta| order | 19266 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C13 |
| direct product | C19⋊C3×C13⋊D13 |
| Fitting, socle, derived, Hall | C132×C19 ⋊ C2×C3 |
| Hall | C132×C19⋊C3 ⋊ C2 |
| Hall | C19×C13⋊D13 ⋊ C3 |
| Sylow | C132 ⋊ C2×C19⋊C3 |
| Sylow | C19 ⋊ C3×C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C19 | C2×C3 |
| LCS | G ▷ C132×C19 | |
| UCS | C1 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3211 |
774 conjugacy classes. The character table is too large to display.
| maximal subgroup of | ((C19⋊C3)⋊D13)⋊D13, D132×C19⋊C3, D19⋊C3×C13⋊D13, … |
| maximal normal subgroup of | ((C19⋊C3)⋊D13)⋊D13, D132×C19⋊C3, D19⋊C3×C13⋊D13, … |
| maximal quotient of | C19⋊C3×#10621725, C2×C19⋊C3×C13⋊D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19266, 78);