Finite Group DatabasebetaFinite Group Databasebeta| order | 27642 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D813 |
| unambiguous semidirect product | C3⋊(C17×D271) |
| unambiguous semidirect product | C271⋊(D3×C17) |
| Fitting, socle, Hall | C3×C17×C271 ⋊ C2 |
| derived, Hall | C3×C271 ⋊ C2×C17 |
| Hall | C17×C271 ⋊ D3 |
| Sylow | C271 ⋊ D3×C17 |
| Hall | C3×C17 ⋊ D271 |
| Sylow | C3 ⋊ C17×D271 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D813 |
| commutator, cosocle, hypocenter | C3×C271 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C17×C271 | C2 |
| LCS | G ▷ C3×C271 | |
| UCS | C1 ◁ C17 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13821 |
6936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27642, 7);