Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#63391 |
| Hall | C5×C9 ⋊ #100 |
| Sylow | C9 ⋊ C5×#100 |
138 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 360 |
A minimal faithful permutation representation — 2 generators on 22 points:
(1,2,3,4,5)(6,11,13,12,7,9,8,14,10)(16,19)(17,21);(7,9)(8,12)(10,11)(13,14)(15,16,17,20,18,19,21,22)255 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 151);