Finite Group DatabasebetaFinite Group Databasebeta| order | 1920 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×Dic3×#170 |
| derived, Hall | C3×C5 ⋊ C22×C4×C8 |
| Sylow | C5 ⋊ C22×C8×Dic3 |
| Sylow | C3 ⋊ C22×C4×#170 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D3×AGL(1,𝔽5) |
| commutator, hypocenter | C3×C5 | C22×C4×C8 |
| Frattini | C22 | C22×D3×AGL(1,𝔽5) |
| Fitting, socle, prime radical | C24×C3×C5 | C2×C4 |
| cosocle | C2×C3×Dic5 | C24 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C24 | |
1520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1920 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1920, 136885);