Finite Group DatabasebetaFinite Group Databasebeta| order | 31407 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C19×C29 · Schur multiplier (H2) = C1 |
| direct product | C19×C29×C19⋊C3 |
| unambiguous semidirect product | C19⋊(C3×C19×C29) |
| unambiguous semidirect product | (C19×C29)⋊(C3×C19) |
| Fitting, socle, Hall | C192×C29 ⋊ C3 |
| derived | C19 ⋊ C3×C19×C29 |
| Sylow | C192 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19×C29 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C3×C19×C29 |
| Frattini | C1 | G |
| Fitting, socle | C192×C29 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C19×C29 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1653 |
4959 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31407, 4);