Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#3990 |
| Hall | C5×C9 ⋊ M32 |
| Sylow | C5 ⋊ C9×M32 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 720 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,3,4,5,6,7,8,9)(10,11,12,14,13)(15,17,19,26,20,18,25,27)(16,21,22,28,23,24,29,30);(11,12,13,14)(15,16,18,21,19,22,27,28,20,23,17,24,25,29,26,30)252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 270);