Finite Group DatabasebetaFinite Group Databasebeta| order | 19314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D29×#66526 |
| unambiguous semidirect product | C29⋊(C2×#66526) |
| Fitting, socle, derived, Hall | C29×C37 ⋊ C2×C9 |
| Hall | C29×#66526 ⋊ C2 |
| Hall | C37×D29 ⋊ C9 |
| Sylow | C37 ⋊ C9×D29 |
| Sylow | C29 ⋊ C2×#66526 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C37 | C2×C9 |
| prime radical | D29×C37⋊C3 | C3 |
| cosocle | C29×C37⋊C3 | C2×C3 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1073 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #50311194, #1181×#66526, D29×#66526⋊C2, … |
| maximal normal subgroup of | #50311194, #1181×#66526, D29×#66526⋊C2, … |
| maximal quotient of | Dic29×#66526, C2×D29×#66526 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19314, 16);