Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×#4078 |
| Fitting | C2×C32×C5×D4 ⋊ C2 |
| Hall | C32×C5 ⋊ AGL(1,ℤ/8) |
| Sylow | C5 ⋊ C32×AGL(1,ℤ/8) |
408 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 174 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 — 3 generators on 19 points:
(1,2,3)(7,8,10,11,9)(13,18)(14,15)(17,19);(4,5,6)(12,14,16,15)(13,17,19,18);(8,9)(10,11)(12,13)(14,17)(15,18)(16,19)279 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4179);