Finite Group DatabasebetaFinite Group Databasebeta| order | 31407 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×C361⋊C3 |
| unambiguous semidirect product | C361⋊(C3×C29) |
| unambiguous semidirect product | (C29×C361)⋊C3 |
| Fitting, Hall | C29×C361 ⋊ C3 |
| derived, Sylow | C361 ⋊ C3×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | C361⋊C3 |
| commutator, cosocle, hypocenter | C361 | C3×C29 |
| Frattini | C19 | C29×C19⋊C3 |
| Fitting | C29×C361 | C3 |
| socle | C19×C29 | C19⋊C3 |
| LCS | G ▷ C361 | |
| UCS | C1 ◁ C29 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10469 |
3567 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31407, 2);