Finite Group DatabasebetaFinite Group Databasebeta| order | 34476 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C132 · Schur multiplier (H2) = C13 |
| direct product | C132×Dic51 |
| unambiguous semidirect product | C3⋊(C132×Dic17) |
| derived, Hall | C3×C17 ⋊ C4×C132 |
| Hall | C3×C132×C17 ⋊ C4 |
| Hall | C132×C17 ⋊ Dic3 |
| Hall | C3×C132 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic3×C132 |
| Sylow | C3 ⋊ C132×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C132 | D51 |
| commutator, hypocenter | C3×C17 | C4×C132 |
| Frattini | C2 | C132×D51 |
| Fitting, socle, prime radical | C2×C3×C132×C17 | C2 |
| cosocle | C2×C3×C17 | C2×C132 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C2×C132 | |
192 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, 80);