Finite Group DatabasebetaFinite Group Databasebeta| order | 19092 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×(C43⋊C3)⋊C4 |
| unambiguous semidirect product | (C43⋊C3)⋊(C4×C37) |
| unambiguous semidirect product | Dic43⋊(C3×C37) |
| derived, Sylow | C43 ⋊ C3×C4×C37 |
| Hall | C37×Dic43 ⋊ C3 |
| Hall | C37×C43⋊C3 ⋊ C4 |
| Hall | C37×C43 ⋊ C3×C4 |
| Hall | Dic43 ⋊ C3×C37 |
| Hall | C43⋊C3 ⋊ C4×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | D43⋊C3 |
| commutator, hypocenter | C43 | C3×C4×C37 |
| Frattini | C2 | C37×D43⋊C3 |
| Fitting, socle | C2×C37×C43 | C2×C3 |
| prime radical | C2×C37×C43⋊C3 | C2 |
| cosocle | C2×C43 | C2×C3×C37 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6364 |
962 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19092, 13);