Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C2 |
| direct product | AGL(1,𝔽5)×#95⋊C3 |
| unambiguous semidirect product | (AGL(1,𝔽5)×#95)⋊C3 |
| Fitting, derived | C5×#95 ⋊ C3×C4 |
| Hall | AGL(1,𝔽5)×#95 ⋊ C3 |
| Sylow | C5 ⋊ C4×#95⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | AGL(1,𝔽5)×C42⋊C3 |
| commutator, Fitting, hypocenter | C5×#95 | C3×C4 |
| Frattini | C23 | A4×AGL(1,𝔽5) |
| socle | C23×C5 | C4×A4 |
| prime radical | D5×#95⋊C3 | C2 |
| cosocle | D5×#95 | C2×C3 |
| LCS | G ▷ C5×#95 | |
| UCS | C1 ◁ C2 | |
314 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 237292);