Finite Group DatabasebetaFinite Group Databasebeta| order | 34038 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C3 |
| direct product | C61×C3⋊D93 |
| unambiguous semidirect product | C3⋊(C61×D93) |
| unambiguous semidirect product | C31⋊(C3⋊D3×C61) |
| Fitting, socle, Hall | C32×C31×C61 ⋊ C2 |
| derived, Hall | C32×C31 ⋊ C2×C61 |
| Hall | C31×C61 ⋊ C3⋊D3 |
| Hall | C32×C61 ⋊ D31 |
| Sylow | C31 ⋊ C3⋊D3×C61 |
| Sylow | C32 ⋊ C61×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | C3⋊D93 |
| commutator, cosocle, hypocenter | C32×C31 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C32×C31×C61 | C2 |
| LCS | G ▷ C32×C31 | |
| UCS | C1 ◁ C61 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17019 |
8601 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34038, 71);