Finite Group DatabasebetaFinite Group Databasebeta| order | 19314 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C3×D29×C37⋊C3 |
| unambiguous semidirect product | C29⋊(C2×C3×C37⋊C3) |
| unambiguous semidirect product | (C37×D29)⋊C32 |
| unambiguous semidirect product | (C3×C37×D29)⋊C3 |
| Fitting, socle | C3×C29×C37 ⋊ C2×C3 |
| derived, Hall | C29×C37 ⋊ C2×C32 |
| Hall | C3×C29×C37⋊C3 ⋊ C2 |
| Hall | C37×D29 ⋊ C32 |
| Sylow | C37 ⋊ C32×D29 |
| Sylow | C29 ⋊ C2×C3×C37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D29×C37⋊C3 |
| commutator, cosocle, hypocenter | C29×C37 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C3×C29×C37 | C2×C3 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3219 |
720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#16864282⋊C3, C3×C37⋊C3×#1181, C3×D29×D37⋊C3, … |
| maximal normal subgroup of | C3×#16864282⋊C3, C3×C37⋊C3×#1181, C3×D29×D37⋊C3, … |
| maximal quotient of | C3×C37⋊C3×Dic29, C2×C3×D29×C37⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19314, 20);