Finite Group DatabasebetaFinite Group Databasebeta| order | 19044 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×Dic1587 |
| unambiguous semidirect product | C3⋊(C3×Dic529) |
| unambiguous semidirect product | C529⋊(C3×Dic3) |
| derived | C3×C529 ⋊ C3×C4 |
| Hall | C32×C529 ⋊ C4 |
| Sylow | C529 ⋊ C3×Dic3 |
| Sylow | C32 ⋊ Dic529 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D1587 |
| commutator, hypocenter | C3×C529 | C3×C4 |
| Frattini | C2×C23 | C3×D69 |
| Fitting | C2×C32×C529 | C2 |
| socle, prime radical | C2×C32×C23 | D23 |
| cosocle | C2×C3×C529 | C2×C3 |
| LCS | G ▷ C3×C529 | |
| UCS | C1 ◁ C2×C3 | |
42 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6348 |
4770 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19044, 14);