Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #226 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×#859 |
| derived | SL(2,𝔽3) ⋊ C3×C4×C5 |
126 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C5×(PSU(3,𝔽2)⋊C3)⋊C4, C3×C4×C5×GL(2,𝔽3) |
| maximal normal subgroup of | C3×C4×C5×GL(2,𝔽3) |
| maximal quotient of | C3×C5×(PSU(3,𝔽2)⋊C3)⋊C4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2523);