Finite Group DatabasebetaFinite Group Databasebeta| order | 32742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C107 · Schur multiplier (H2) = C1 |
| direct product | C3×D51×C107 |
| unambiguous semidirect product | C3⋊(C3×D17×C107) |
| unambiguous semidirect product | C17⋊(C3×D3×C107) |
| Fitting, socle, Hall | C32×C17×C107 ⋊ C2 |
| derived | C3×C17 ⋊ C2×C3×C107 |
| Hall | C17×C107 ⋊ C3×D3 |
| Hall | C32×C107 ⋊ D17 |
| Hall | C32×C17 ⋊ C2×C107 |
| Sylow | C17 ⋊ C3×D3×C107 |
| Sylow | C32 ⋊ D17×C107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C107 | D51 |
| commutator, cosocle, hypocenter | C3×C17 | C2×C3×C107 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C107 | C2 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C3×C107 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10914 |
8667 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32742, 15);