Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | AGL(1,𝔽5)×C3⋊C32 |
| unambiguous semidirect product | (C3×AGL(1,𝔽5))⋊C32 |
| derived, Hall | C3×C5 ⋊ C4×C32 |
| Sylow | C5 ⋊ C4×C3⋊C32 |
| Sylow | C3 ⋊ AGL(1,𝔽5)×C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C4×C32 |
| Fitting | C3×C5×C16 | C2×C4 |
| socle | C2×C3×C5 | C4×C16 |
| prime radical | C2×C3×D5 | C2×C16 |
| cosocle | C3×D5×C16 | C22 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C16 | |
144 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 4893);