Finite Group DatabasebetaFinite Group Databasebeta| order | 34026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C53 · Schur multiplier (H2) = C1 |
| direct product | D3×C107⋊C53 |
| unambiguous semidirect product | C3⋊(C2×C107⋊C53) |
| unambiguous semidirect product | (D3×C107)⋊C53 |
| Fitting, socle, derived, Hall | C3×C107 ⋊ C2×C53 |
| Hall | C3×C107⋊C53 ⋊ C2 |
| Hall | D3×C107 ⋊ C53 |
| Sylow | C107 ⋊ D3×C53 |
| Sylow | C3 ⋊ C2×C107⋊C53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C107 | C2×C53 |
| LCS | G ▷ C3×C107 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 321 |
165 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34026, 11);