Finite Group DatabasebetaFinite Group Databasebeta| order | 19620 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×#11758281⋊C2 |
| unambiguous semidirect product | #11758281⋊(C22×C5) |
| unambiguous semidirect product | (C2×#11758281)⋊(C2×C5) |
| Fitting, socle | C2×C5×C109 ⋊ C2×C9 |
| derived, Sylow | C109 ⋊ C22×C5×C9 |
| Hall | C5×#11758281 ⋊ C22 |
| Hall | C2×C5×D109 ⋊ C9 |
| Hall | #11758281 ⋊ C22×C5 |
| Hall | C5×C109 ⋊ C22×C9 |
| Hall | C2×D109 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | #11758281⋊C2 |
| commutator, hypocenter | C109 | C22×C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C109 | C2×C9 |
| prime radical | C2×C5×D109⋊C3 | C3 |
| cosocle | C109⋊C3 | C22×C3×C5 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C5 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1090 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19620, 85);