Finite Group DatabasebetaFinite Group Databasebeta| order | 31842 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊(D61⋊C9) |
| unambiguous semidirect product | (C61⋊C9)⋊D29 |
| unambiguous semidirect product | D1769⋊C9 |
| derived, Hall | C29×C61 ⋊ C2×C9 |
| Hall | C29×C61⋊C9 ⋊ C2 |
| Hall | D1769 ⋊ C9 |
| Hall | C61⋊C9 ⋊ D29 |
| Sylow | C61 ⋊ C9×D29 |
| Sylow | C29 ⋊ D61⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C29⋊(D61⋊C3) |
| commutator, hypocenter | C29×C61 | C2×C9 |
| Fitting, socle, cosocle | C3×C29×C61 | C2×C3 |
| prime radical | C3×D1769 | C3 |
| LCS | G ▷ C29×C61 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15921 |
Polycyclic presentation:
2,3,29,61,3|b^3=e,c^a=c^28,d^a=d^60,d^b=d^471014 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31842, 12);