Finite Group DatabasebetaFinite Group Databasebeta| order | 19314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C37 · Schur multiplier (H2) = C1 |
| direct product | C3×C37×D87 |
| unambiguous semidirect product | C3⋊(C3×C37×D29) |
| unambiguous semidirect product | C29⋊(C3×D3×C37) |
| Fitting, socle, Hall | C32×C29×C37 ⋊ C2 |
| derived | C3×C29 ⋊ C2×C3×C37 |
| Hall | C29×C37 ⋊ C3×D3 |
| Hall | C32×C37 ⋊ D29 |
| Hall | C32×C29 ⋊ C2×C37 |
| Sylow | C29 ⋊ C3×D3×C37 |
| Sylow | C32 ⋊ C37×D29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C37 | D87 |
| commutator, cosocle, hypocenter | C3×C29 | C2×C3×C37 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C37 | C2 |
| LCS | G ▷ C3×C29 | |
| UCS | C1 ◁ C3×C37 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6438 |
4995 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D37×D87, C3×D3×C37×D29, C3×D87⋊D37, … |
| maximal normal subgroup of | C3×D37×D87, C3×D3×C37×D29, C3×D87⋊D37, … |
| maximal quotient of | C3×C37×Dic87, C2×C3×C37×D87 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19314, 31);