Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4 · Schur multiplier (H2) = C215 |
| Fitting, socle | C24×C3×C5 ⋊ C2×C4 |
| derived, Hall | C3×C5 ⋊ C25×C4 |
| Sylow | C5 ⋊ C24×C4×D3 |
| Sylow | C3 ⋊ C25×AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C25×C4 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3×C5 | C2×C4 |
| prime radical | C24×D3×D5 | C2 |
| cosocle | C3×D5 | C26 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C24 | |
21104 conjugacy classes of subgroups; only the 6398 normal subgroups are shown.
This group has 21104 conjugacy classes of subgroups — too many to draw. Only its 6398 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236168);