Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C42 · Schur multiplier (H2) = C23×C3 |
| direct product | C32×(C2×AGL(1,𝔽5))⋊C4 |
| unambiguous semidirect product | (C2×AGL(1,𝔽5))⋊(C32×C4) |
| Fitting | C2×C32×C4×C5 ⋊ C4 |
| Hall | C32×C5 ⋊ #95 |
| Sylow | C5 ⋊ C32×#95 |
456 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 360 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(7,8,9,11,10)(12,13,14,15)(17,19);(4,5,6)(8,9,10,11)(16,17)(18,19)252 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#65779, C32×#65699, C32×C22⋊C4×AGL(1,𝔽5), … |
| maximal normal subgroup of | C32×#65779, C32×#65699, C32×C22⋊C4×AGL(1,𝔽5), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2575);