Finite Group DatabasebetaFinite Group Databasebeta| order | 19314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C3 |
| direct product | C37×C3⋊D87 |
| unambiguous semidirect product | C3⋊(C37×D87) |
| unambiguous semidirect product | C29⋊(C3⋊D3×C37) |
| Fitting, socle, Hall | C32×C29×C37 ⋊ C2 |
| derived, Hall | C32×C29 ⋊ C2×C37 |
| Hall | C29×C37 ⋊ C3⋊D3 |
| Hall | C32×C37 ⋊ D29 |
| Sylow | C29 ⋊ C3⋊D3×C37 |
| Sylow | C32 ⋊ C37×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | C3⋊D87 |
| commutator, cosocle, hypocenter | C32×C29 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C37 | C2 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 ◁ C37 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9657 |
4884 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C37×#11760329, #50311236, D3×C37×D87, … |
| maximal normal subgroup of | C37×#11760329, #50311236, D3×C37×D87, … |
| maximal quotient of | C37×C3⋊Dic87, C2×C37×C3⋊D87 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19314, 27);