Finite Group DatabasebetaFinite Group Databasebeta| order | 29790 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D331⋊C9) |
| unambiguous semidirect product | (C331⋊C9)⋊D5 |
| unambiguous semidirect product | D1655⋊C9 |
| derived, Hall | C5×C331 ⋊ C2×C9 |
| Hall | C5×C331⋊C9 ⋊ C2 |
| Hall | D1655 ⋊ C9 |
| Hall | C331⋊C9 ⋊ D5 |
| Sylow | C331 ⋊ C9×D5 |
| Sylow | C5 ⋊ D331⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(D331⋊C3) |
| commutator, hypocenter | C5×C331 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C331 | C2×C3 |
| prime radical | C3×D1655 | C3 |
| LCS | G ▷ C5×C331 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 14895 |
Polycyclic presentation:
2,3,5,331,3|b^3=e,c^a=c^4,d^a=d^330,d^b=d^299861 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29790, 17);