Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D3×D2873 |
| unambiguous semidirect product | (D3×C17)⋊D169 |
| unambiguous semidirect product | (D3×C169)⋊D17 |
| Fitting, derived, Hall | C3×C17×C169 ⋊ C22 |
| Hall | C17×C169 ⋊ C2×D3 |
| Hall | C3×C169 ⋊ C2×D17 |
| Sylow | C169 ⋊ D3×D17 |
| Hall | C3×C17 ⋊ C2×D169 |
| Sylow | C17 ⋊ D3×D169 |
| Sylow | C3 ⋊ C2×D2873 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C3×C17×C169 | C22 |
| Frattini | C13 | D3×D221 |
| socle | C3×C13×C17 | C2×D13 |
| LCS | G ▷ C3×C17×C169 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8619 |
4314 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 41);