Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×A4×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | D3×A4×AGL(1,𝔽5) |
| unambiguous semidirect product | (C3×AGL(1,𝔽5))⋊(C2×A4) |
| unambiguous semidirect product | ΓL(1,𝔽16)⋊(C2×A4) |
| unambiguous semidirect product | (C22×D3×AGL(1,𝔽5))⋊C3 |
| Fitting, socle, derived | C22×C3×C5 ⋊ C2×C3×C4 |
| Sylow | C5 ⋊ C4×D3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C22×C3×C5 | C2×C3×C4 |
| prime radical | D3×D5×A4 | C2 |
| cosocle | C22×C3×D5 | C22×C3 |
| LCS | G ▷ C22×C3×C5 | |
| UCS | C1 | |
276 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 42 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(1440, 5870);