Finite Group DatabasebetaFinite Group Databasebeta| order | 34038 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D5673 |
| unambiguous semidirect product | C31⋊(C3⋊D183) |
| unambiguous semidirect product | C61⋊(C3⋊D93) |
| Fitting, socle, derived, Hall | C32×C31×C61 ⋊ C2 |
| Hall | C31×C61 ⋊ C3⋊D3 |
| Hall | C32×C61 ⋊ D31 |
| Hall | C32×C31 ⋊ D61 |
| Sylow | C61 ⋊ C3⋊D93 |
| Sylow | C31 ⋊ C3⋊D183 |
| Sylow | C32 ⋊ D1891 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C31×C61 | C2 |
| LCS | G ▷ C32×C31×C61 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17019 |
Polycyclic presentation:
2,3^2,31,61|b^a=b^2,c^a=c^2,d^a=d^30,e^a=e^608511 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34038, 72);