Finite Group DatabasebetaFinite Group Databasebeta| order | 19620 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C5×C22⋊#11758281 |
| unambiguous semidirect product | C22⋊(C5×#11758281) |
| unambiguous semidirect product | (C22×C5)⋊#11758281 |
| Fitting, socle, Hall | C22×C5×C109 ⋊ C9 |
| derived, Hall | C22×C109 ⋊ C5×C9 |
| Hall | C5×C109 ⋊ C22⋊C9 |
| Sylow | C109 ⋊ C5×C22⋊C9 |
| Hall | C22×C5 ⋊ #11758281 |
| Sylow | C22 ⋊ C5×#11758281 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C22⋊#11758281 |
| commutator, hypocenter | C22×C109 | C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C109 | C9 |
| prime radical | C22×C5×C109⋊C3 | C3 |
| cosocle | C22×C109⋊C3 | C3×C5 |
| LCS | G ▷ C22×C109 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2180 |
300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19620, 108);