Finite Group DatabasebetaFinite Group Databasebeta| order | 19620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×#11758281 |
| Fitting, socle, derived, Hall | C5×C109 ⋊ C4×C9 |
| Hall | C5×#11758281 ⋊ C4 |
| Hall | AGL(1,𝔽5)×C109 ⋊ C9 |
| Sylow | C109 ⋊ C9×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#11758281 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C109 | C4×C9 |
| prime radical, cosocle | D5×C109⋊C3 | C2×C3 |
| LCS | G ▷ C5×C109 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 545 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19620, 82);