Finite Group DatabasebetaFinite Group Databasebeta| order | 31842 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C61 · Schur multiplier (H2) = C3 |
| direct product | C61×C3⋊D87 |
| unambiguous semidirect product | C3⋊(C61×D87) |
| unambiguous semidirect product | C29⋊(C3⋊D3×C61) |
| Fitting, socle, Hall | C32×C29×C61 ⋊ C2 |
| derived, Hall | C32×C29 ⋊ C2×C61 |
| Hall | C29×C61 ⋊ C3⋊D3 |
| Hall | C32×C61 ⋊ D29 |
| Sylow | C29 ⋊ C3⋊D3×C61 |
| Sylow | C32 ⋊ D29×C61 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C61 | C3⋊D87 |
| commutator, cosocle, hypocenter | C32×C29 | C2×C61 |
| Frattini | C1 | G |
| Fitting, socle | C32×C29×C61 | C2 |
| LCS | G ▷ C32×C29 | |
| UCS | C1 ◁ C61 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15921 |
8052 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31842, 31);