Finite Group DatabasebetaFinite Group Databasebeta| order | 32742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C107 · Schur multiplier (H2) = C1 |
| direct product | C107×D153 |
| unambiguous semidirect product | C9⋊(D17×C107) |
| unambiguous semidirect product | C17⋊(D9×C107) |
| Fitting, Hall | C9×C17×C107 ⋊ C2 |
| derived, Hall | C9×C17 ⋊ C2×C107 |
| Hall | C17×C107 ⋊ D9 |
| Hall | C9×C107 ⋊ D17 |
| Sylow | C17 ⋊ D9×C107 |
| Sylow | C9 ⋊ D17×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C107 | D153 |
| commutator, cosocle, hypocenter | C9×C17 | C2×C107 |
| Frattini | C3 | D51×C107 |
| Fitting | C9×C17×C107 | C2 |
| socle | C3×C17×C107 | D3 |
| LCS | G ▷ C9×C17 | |
| UCS | C1 ◁ C107 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16371 |
8346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32742, 7);