Finite Group DatabasebetaFinite Group Databasebeta| order | 1900 |
| isoclinism | isoclinic class of C19⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×C19⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C19⋊(C5×AGL(1,𝔽5)) |
| Fitting, socle, Hall | C52×C19 ⋊ C4 |
| derived | C5×C19 ⋊ C4×C5 |
| Sylow | C52 ⋊ Dic19 |
| Sylow | C19 ⋊ C5×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C19⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C19 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C19 | C4 |
| prime radical | C5×D5×C19 | C2 |
| cosocle | D5×C19 | C2×C5 |
| LCS | G ▷ C5×C19 | |
| UCS | C1 ◁ C5 | |
26 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 380 |
205 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1900, 19);