Finite Group DatabasebetaFinite Group Databasebeta| order | 34038 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31×C61 · Schur multiplier (H2) = C1 |
| direct product | D9×C31×C61 |
| unambiguous semidirect product | C9⋊(C2×C31×C61) |
| Fitting, Hall | C9×C31×C61 ⋊ C2 |
| derived, Sylow | C9 ⋊ C2×C31×C61 |
| Hall | C9×C61 ⋊ C2×C31 |
| Hall | C9×C31 ⋊ C2×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31×C61 | D9 |
| commutator, cosocle, hypocenter | C9 | C2×C31×C61 |
| Frattini | C3 | D3×C31×C61 |
| Fitting | C9×C31×C61 | C2 |
| socle | C3×C31×C61 | D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C31×C61 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17019 |
11346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34038, 9);