Finite Group DatabasebetaFinite Group Databasebeta| order | 31410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×D349⋊C9 |
| unambiguous semidirect product | D349⋊(C5×C9) |
| unambiguous semidirect product | (C349⋊C9)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D349)⋊C9 |
| derived, Sylow | C349 ⋊ C2×C5×C9 |
| Hall | C5×C349⋊C9 ⋊ C2 |
| Hall | C5×D349 ⋊ C9 |
| Hall | C349⋊C9 ⋊ C2×C5 |
| Hall | C5×C349 ⋊ C2×C9 |
| Hall | D349 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D349⋊C3 |
| commutator, hypocenter | C349 | C2×C5×C9 |
| Frattini | C3 | C5×D349⋊C3 |
| Fitting, socle | C3×C5×C349 | C2×C3 |
| prime radical | C3×C5×D349 | C3 |
| cosocle | C3×C349 | C2×C3×C5 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15705 |
960 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31410, 10);