Finite Group DatabasebetaFinite Group Databasebeta| order | 34038 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C61⋊C9)⋊D31 |
| derived, Hall | C31×C61 ⋊ C2×C9 |
| Hall | C31×C61⋊C9 ⋊ C2 |
| Hall | D1891 ⋊ C9 |
| Hall | C61⋊C9 ⋊ D31 |
| Sylow | C61 ⋊ C9×D31 |
| Sylow | C31 ⋊ D61⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C61⋊C3)⋊D31 |
| commutator, hypocenter | C31×C61 | C2×C9 |
| Fitting, socle, cosocle | C3×C31×C61 | C2×C3 |
| prime radical | C3×D1891 | C3 |
| LCS | G ▷ C31×C61 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17019 |
Polycyclic presentation:
2,3,31,61,3|b^3=e,c^a=c^30,d^a=d^60,d^b=d^471083 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34038, 21);