Finite Group DatabasebetaFinite Group Databasebeta| order | 34026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C53 · Schur multiplier (H2) = C1 |
| direct product | C3×AGL(1,𝔽107) |
| unambiguous semidirect product | D107⋊(C3×C53) |
| unambiguous semidirect product | (C3×D107)⋊C53 |
| unambiguous semidirect product | (C107⋊C53)⋊(C2×C3) |
| Fitting, socle, Hall | C3×C107 ⋊ C2×C53 |
| derived, Sylow | C107 ⋊ C2×C3×C53 |
| Hall | C3×C107⋊C53 ⋊ C2 |
| Hall | C107⋊C53 ⋊ C2×C3 |
| Hall | C3×D107 ⋊ C53 |
| Hall | D107 ⋊ C3×C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | AGL(1,𝔽107) |
| commutator, cosocle, hypocenter | C107 | C2×C3×C53 |
| Frattini | C1 | G |
| Fitting, socle | C3×C107 | C2×C53 |
| LCS | G ▷ C107 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 321 |
321 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34026, 10);