Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3×C4 · Schur multiplier (H2) = C215 |
| direct product | C25×C3×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C24×C3×C4) |
| Fitting, socle | C25×C3×C5 ⋊ C4 |
| derived, Sylow | C5 ⋊ C25×C3×C4 |
| Hall | C3×C5 ⋊ C25×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25×C3 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C25×C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C25×C3×C5 | C4 |
| prime radical | C25×C3×D5 | C2 |
| cosocle | D5 | C26×C3 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C25×C3 | |
21104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 480 |
480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C3×AGL(1,𝔽5)×#120, C24×AGL(1,𝔽5)×AGL(1,𝔽7) |
| maximal normal subgroup of | C2×C3×AGL(1,𝔽5)×#120 |
| maximal quotient of | C24×AGL(1,𝔽5)×AGL(1,𝔽7) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 236162);