Finite Group DatabasebetaFinite Group Databasebeta| order | 31842 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D87×C61⋊C3 |
| unambiguous semidirect product | C3⋊(D29×C61⋊C3) |
| unambiguous semidirect product | C29⋊(D3×C61⋊C3) |
| unambiguous semidirect product | (C61×D87)⋊C3 |
| Fitting, socle, derived | C3×C29×C61 ⋊ C2×C3 |
| Hall | C3×C29×C61⋊C3 ⋊ C2 |
| Hall | C29×C61 ⋊ C3×D3 |
| Hall | C3×C61⋊C3 ⋊ D29 |
| Sylow | C61 ⋊ C3×D87 |
| Sylow | C29 ⋊ D3×C61⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C29×C61 | C2×C3 |
| LCS | G ▷ C3×C29×C61 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5307 |
1035 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31842, 20);