Finite Group DatabasebetaFinite Group Databasebeta| order | 20610 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×C5×C229⋊C9 |
| unambiguous semidirect product | (C2×C229)⋊(C5×C9) |
| unambiguous semidirect product | (C2×C5×C229)⋊C9 |
| derived, Sylow | C229 ⋊ C2×C5×C9 |
| Hall | C2×C5×C229 ⋊ C9 |
| Hall | C5×C229 ⋊ C2×C9 |
| Hall | C2×C229 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | C229⋊C3 |
| commutator, hypocenter | C229 | C2×C5×C9 |
| Frattini | C3 | C2×C5×C229⋊C3 |
| Fitting, socle, prime radical | C2×C3×C5×C229 | C3 |
| cosocle | C3×C229 | C2×C3×C5 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C2×C3×C5 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20610 |
2370 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20610, 2);