Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of AΓL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×GO+(4,𝔽2)⋊C4 |
| unambiguous semidirect product | GO+(4,𝔽2)⋊(C4×C5) |
| Hall | C32×C5 ⋊ #102 |
| Sylow | C32 ⋊ C5×#102 |
132 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 18 points:
(1,2,3,4,5)(6,11,13)(7,10,12,9,14,8);(7,8,9,13,10,12,14,11)(15,16,17,18)90 conjugacy classes — view the full character table.
| maximal subgroup of | C4×C5×AΓL(1,𝔽9), C3×C5×GO+(4,𝔽2)⋊C4 |
| maximal normal subgroup of | C4×C5×AΓL(1,𝔽9), C3×C5×GO+(4,𝔽2)⋊C4 |
| maximal quotient of | C3×C5×GO+(4,𝔽2)⋊C4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4707);