Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C169 · Schur multiplier (H2) = C1 |
| direct product | C169×Dic51 |
| unambiguous semidirect product | C3⋊(Dic17×C169) |
| derived, Hall | C3×C17 ⋊ C4×C169 |
| Hall | C3×C17×C169 ⋊ C4 |
| Hall | C17×C169 ⋊ Dic3 |
| Hall | C3×C169 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic3×C169 |
| Sylow | C3 ⋊ Dic17×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C169 | D51 |
| commutator, hypocenter | C3×C17 | C4×C169 |
| Frattini | C2×C13 | C13×D51 |
| Fitting | C2×C3×C17×C169 | C2 |
| socle, prime radical, cosocle | C2×C3×C13×C17 | C2×C13 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C169 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 34476 |
9126 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34476, 10);