Finite Group DatabasebetaFinite Group Databasebeta| order | 31410 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D349⋊C9) |
| unambiguous semidirect product | (C349⋊C9)⋊D5 |
| unambiguous semidirect product | D1745⋊C9 |
| derived, Hall | C5×C349 ⋊ C2×C9 |
| Hall | C5×C349⋊C9 ⋊ C2 |
| Hall | D1745 ⋊ C9 |
| Hall | C349⋊C9 ⋊ D5 |
| Sylow | C349 ⋊ C9×D5 |
| Sylow | C5 ⋊ D349⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(D349⋊C3) |
| commutator, hypocenter | C5×C349 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C349 | C2×C3 |
| prime radical | C3×D1745 | C3 |
| LCS | G ▷ C5×C349 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 15705 |
Polycyclic presentation:
2,3,5,349,3|b^3=e,c^a=c^4,d^a=d^348,d^b=d^226906 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31410, 12);