Finite Group DatabasebetaFinite Group Databasebeta| order | 20610 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊(D229⋊C9) |
| unambiguous semidirect product | (C229⋊C9)⋊D5 |
| unambiguous semidirect product | D1145⋊C9 |
| derived, Hall | C5×C229 ⋊ C2×C9 |
| Hall | C5×C229⋊C9 ⋊ C2 |
| Hall | D1145 ⋊ C9 |
| Hall | C229⋊C9 ⋊ D5 |
| Sylow | C229 ⋊ C9×D5 |
| Sylow | C5 ⋊ D229⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C5⋊(D229⋊C3) |
| commutator, hypocenter | C5×C229 | C2×C9 |
| Fitting, socle, cosocle | C3×C5×C229 | C2×C3 |
| prime radical | C3×D1145 | C3 |
| LCS | G ▷ C5×C229 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 10305 |
Polycyclic presentation:
2,3,5,229,3|b^3=e,c^a=c^4,d^a=d^228,d^b=d^134606 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20610, 12);