Finite Group DatabasebetaFinite Group Databasebeta| order | 34596 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×Dic31⋊C9 |
| unambiguous semidirect product | Dic31⋊(C9×C31) |
| unambiguous semidirect product | (C31⋊C9)⋊(C4×C31) |
| derived | C31 ⋊ C4×C9×C31 |
| Hall | C31×C31⋊C9 ⋊ C4 |
| Hall | C31×Dic31 ⋊ C9 |
| Sylow | C312 ⋊ C4×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C31 | D31⋊C3 |
| commutator, hypocenter | C31 | C4×C9×C31 |
| Frattini | C2×C3 | C31×D31⋊C3 |
| Fitting, socle, prime radical | C2×C3×C312 | C2×C3 |
| cosocle | C2×C3×C31 | C2×C3×C31 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C3×C31 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1116 |
2046 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34596, 48);