Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of Dic36 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#63380 |
| Fitting | C2×C5×C8×C9 ⋊ C2 |
| Hall | C5×C9 ⋊ #102 |
| Sylow | C9 ⋊ C5×#102 |
150 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 720 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5)(6,7,10,12,14,13,8,11,9)(15,16,17,18)(19,20,21,23,22,24,25,26);(7,9)(8,12)(10,11)(13,14)(20,23)(21,25)(24,26)390 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 140);