Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of AGL(1,𝔽16) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C23×AGL(1,𝔽16) |
| unambiguous semidirect product | (C23×C22⋊A4)⋊C5 |
| Fitting, socle, Sylow | C27 ⋊ C3×C5 |
| derived | C24 ⋊ C23×C3×C5 |
| Hall | C23×C24⋊C5 ⋊ C3 |
| Hall | C23×C22⋊A4 ⋊ C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | AGL(1,𝔽16) |
| commutator, cosocle, hypocenter | C24 | C23×C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C27 | C3×C5 |
| LCS | G ▷ C24 | |
| UCS | C1 ◁ C23 | |
2100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 240400);