Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C3⋊D3×AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C3×C4 |
| direct product | C4×C3⋊D3×AGL(1,𝔽5) |
| Fitting | C32×C4×C5 ⋊ C2×C4 |
| derived, Hall | C32×C5 ⋊ C2×C42 |
| Sylow | C32 ⋊ C2×C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C42×C3⋊D3 |
648 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4989);