Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#63930 |
| Hall | C32×C5 ⋊ C2×SD16 |
| Sylow | C32 ⋊ C2×C5×SD16 |
326 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 120 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,3,4,5)(7,11)(8,12)(9,13)(14,15,16)(17,18,19);(6,8,10,7)(9,12,13,11)(15,16);(6,7,10,8)(9,11,13,12)(18,19)165 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#63930, C5×#10595100, #72230424 |
| maximal normal subgroup of | D5×#63930, C5×#10595100, #72230424 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3519);