Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#63953 |
| Hall | C32×C5 ⋊ #124 |
| Sylow | C32 ⋊ C5×#124 |
358 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 92 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)(17,21)(20,23);(7,8)(12,13,14,15)(16,18,19,22)(17,20,21,23);(10,11)(12,13,14,15)(16,17)(18,20)(19,21)(22,23)210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3571);