Finite Group DatabasebetaFinite Group Databasebeta| order | 19620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D5×#11758281⋊C2 |
| unambiguous semidirect product | (C5×#11758281⋊C2)⋊C2 |
| unambiguous semidirect product | (C5⋊(#11758281⋊C2))⋊C2 |
| unambiguous semidirect product | (D5×#11758281)⋊C2 |
| Fitting, socle, derived, Hall | C5×C109 ⋊ C22×C9 |
| Hall | C5×#11758281 ⋊ C22 |
| Hall | D5×D109 ⋊ C9 |
| Hall | #11758281 ⋊ C2×D5 |
| Sylow | C109 ⋊ C2×C9×D5 |
| Sylow | C5 ⋊ C2×#11758281⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C109 | C22×C9 |
| prime radical | D5×D109⋊C3 | C3 |
| cosocle | C5×C109⋊C3 | C22×C3 |
| LCS | G ▷ C5×C109 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 545 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19620, 84);