Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#63982 |
| Hall | C32×C5 ⋊ C22⋊Q8 |
| Sylow | C32 ⋊ C5×C22⋊Q8 |
350 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3,4,5)(6,7,8)(9,10,11)(12,13)(14,15);(7,8)(13,15)(16,18,19,23)(17,20,21,22);(10,11)(13,15)(16,17,19,21)(18,22,23,20)210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3570);