Finite Group DatabasebetaFinite Group Databasebeta| order | 34038 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D61⋊C9 |
| unambiguous semidirect product | D61⋊(C9×C31) |
| unambiguous semidirect product | (C61⋊C9)⋊(C2×C31) |
| derived, Sylow | C61 ⋊ C2×C9×C31 |
| Hall | C31×C61⋊C9 ⋊ C2 |
| Hall | C31×D61 ⋊ C9 |
| Hall | C31×C61 ⋊ C2×C9 |
| Hall | C61⋊C9 ⋊ C2×C31 |
| Hall | D61 ⋊ C9×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | D61⋊C3 |
| commutator, hypocenter | C61 | C2×C9×C31 |
| Frattini | C3 | C31×D61⋊C3 |
| Fitting, socle | C3×C31×C61 | C2×C3 |
| prime radical | C3×C31×D61 | C3 |
| cosocle | C3×C61 | C2×C3×C31 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C3×C31 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17019 |
1488 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34038, 13);