Finite Group DatabasebetaFinite Group Databasebeta| order | 19314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D261 |
| unambiguous semidirect product | C9⋊(C37×D29) |
| unambiguous semidirect product | C29⋊(D9×C37) |
| Fitting, Hall | C9×C29×C37 ⋊ C2 |
| derived, Hall | C9×C29 ⋊ C2×C37 |
| Hall | C29×C37 ⋊ D9 |
| Hall | C9×C37 ⋊ D29 |
| Sylow | C29 ⋊ D9×C37 |
| Sylow | C9 ⋊ C37×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D261 |
| commutator, cosocle, hypocenter | C9×C29 | C2×C37 |
| Frattini | C3 | C37×D87 |
| Fitting | C9×C29×C37 | C2 |
| socle | C3×C29×C37 | D3 |
| LCS | G ▷ C9×C29 | |
| UCS | C1 ◁ C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9657 |
4884 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D37×D261, D9×C37×D29, D261⋊D37, … |
| maximal normal subgroup of | D37×D261, D9×C37×D29, D261⋊D37, … |
| maximal quotient of | C37×Dic261, C2×C37×D261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19314, 8);