Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×#91151 |
| Hall | C32×C5 ⋊ #102 |
| Sylow | C32 ⋊ #4007 |
| Sylow | C5 ⋊ C3×#809 |
226 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
99 conjugacy classes — view the full character table.
| maximal subgroup of | #72230413, C3×AGL(1,𝔽5)×#213, #72230419, … |
| maximal normal subgroup of | #72230413, C3×AGL(1,𝔽5)×#213, #72230419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1701);