Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D80 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×#3932 |
| Fitting | C32×C5×C16 ⋊ C2 |
| Hall | C32×C5 ⋊ SD32 |
| Sylow | C5 ⋊ C32×SD32 |
156 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 720 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(7,8,10,11,9)(12,13,18,24,23,27,14,17,16,20,21,26,15,19,22,25);(4,5,6)(8,9)(10,11)(13,17)(14,21)(15,23)(18,22)(19,26)(20,25)(24,27)387 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1235);