Finite Group DatabasebetaFinite Group Databasebeta| order | 34914 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1 |
| direct product | C3×D529⋊C11 |
| unambiguous semidirect product | D529⋊(C3×C11) |
| unambiguous semidirect product | (C3×D529)⋊C11 |
| unambiguous semidirect product | (C529⋊C11)⋊(C2×C3) |
| Fitting, Hall | C3×C529 ⋊ C2×C11 |
| derived, Sylow | C529 ⋊ C2×C3×C11 |
| Hall | C3×C529⋊C11 ⋊ C2 |
| Hall | C529⋊C11 ⋊ C2×C3 |
| Hall | C3×D529 ⋊ C11 |
| Hall | D529 ⋊ C3×C11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D529⋊C11 |
| commutator, cosocle, hypocenter | C529 | C2×C3×C11 |
| Frattini | C23 | C3×AGL(1,𝔽23) |
| Fitting | C3×C529 | C2×C11 |
| socle | C3×C23 | AGL(1,𝔽23) |
| LCS | G ▷ C529 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1587 |
138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34914, 2);