Finite Group DatabasebetaFinite Group Databasebeta| order | 21660 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×(C19⋊C3)⋊AGL(1,𝔽5) |
| unambiguous semidirect product | (C19⋊C3)⋊(C19×AGL(1,𝔽5)) |
| unambiguous semidirect product | (C19⋊AGL(1,𝔽5))⋊(C3×C19) |
| Fitting, socle, Hall | C5×C192 ⋊ C3×C4 |
| derived | C5×C19 ⋊ C3×C4×C19 |
| Hall | C19×C19⋊AGL(1,𝔽5) ⋊ C3 |
| Hall | C5×C19×C19⋊C3 ⋊ C4 |
| Hall | C19×C19⋊C3 ⋊ AGL(1,𝔽5) |
| Sylow | C192 ⋊ C3×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C19×(C19⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | (C19⋊C3)⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C19 | C3×C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C5×C192 | C3×C4 |
| prime radical | D5×C19×C19⋊C3 | C2 |
| cosocle | D5×C19 | C2×C3×C19 |
| LCS | G ▷ C5×C19 | |
| UCS | C1 ◁ C19 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 570 |
513 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21660, 112);