Finite Group DatabasebetaFinite Group Databasebeta| order | 34932 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×C3⋊#4223 |
| unambiguous semidirect product | C3⋊(C71×#4223) |
| Fitting, socle, Hall | C3×C41×C71 ⋊ C4 |
| derived, Hall | C3×C41 ⋊ C4×C71 |
| Hall | C41×C71 ⋊ Dic3 |
| Hall | C3×C71 ⋊ #4223 |
| Sylow | C41 ⋊ Dic3×C71 |
| Sylow | C3 ⋊ C71×#4223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | C3⋊#4223 |
| commutator, hypocenter | C3×C41 | C4×C71 |
| Frattini | C1 | G |
| Fitting, socle | C3×C41×C71 | C4 |
| prime radical | C3×C71×D41 | C2 |
| cosocle | C3×D41 | C2×C71 |
| LCS | G ▷ C3×C41 | |
| UCS | C1 ◁ C71 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8733 |
2556 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34932, 14);