Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C31 · Schur multiplier (H2) = C3 |
| direct product | C31×C31⋊#157 |
| unambiguous semidirect product | C31⋊(C31×#157) |
| Fitting, socle, Hall | C32×C312 ⋊ C4 |
| derived | C32×C31 ⋊ C4×C31 |
| Sylow | C312 ⋊ #157 |
| Sylow | C32 ⋊ C31×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C31⋊#157 |
| commutator, hypocenter | C32×C31 | C4×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C312 | C4 |
| prime radical | C3⋊D3×C312 | C2 |
| cosocle | C3⋊D3×C31 | C2×C31 |
| LCS | G ▷ C32×C31 | |
| UCS | C1 ◁ C31 | |
220 conjugacy classes of subgroups.
| transitive degree | μt(G) = 186 |
2976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 193);