Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×AGL(1,𝔽5)×Dic6 |
| unambiguous semidirect product | (C3×AGL(1,𝔽5))⋊(C3×Q8) |
| Hall | C32×C5 ⋊ C4×Q8 |
| Sylow | C32 ⋊ Q8×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×C4×Dic6 |
310 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
135 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×#214, C3×#11751944, AGL(1,𝔽5)×#3717, … |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×#214, C3×#11751944, AGL(1,𝔽5)×#3717, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4946);