Finite Group DatabasebetaFinite Group Databasebeta| order | 19620 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C3×#14546126⋊C3 |
| unambiguous semidirect product | #14546126⋊C32 |
| unambiguous semidirect product | (C3×#14546126)⋊C3 |
| Fitting, socle | C3×C5×C109 ⋊ C3×C4 |
| derived, Hall | C5×C109 ⋊ C32×C4 |
| Hall | C3×C5×C109⋊C3 ⋊ C4 |
| Hall | #14546126 ⋊ C32 |
| Hall | C3×C109⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C109 ⋊ C32×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×#89137⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14546126⋊C3 |
| commutator, hypocenter | C5×C109 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C109 | C3×C4 |
| prime radical | C3×C5⋊(D109⋊C3) | C2 |
| cosocle | D545 | C2×C32 |
| LCS | G ▷ C5×C109 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1635 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19620, 89);