Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of (C2×D3)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×D5⋊ΓL(1,𝔽25) |
| unambiguous semidirect product | D5⋊(C3×ΓL(1,𝔽25)) |
| Hall | C32×C5 ⋊ C2×M16 |
| Sylow | C32 ⋊ D5⋊M16 |
| Sylow | C5 ⋊ C2×C3×ΓL(1,𝔽25) |
294 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4957);