Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of GO+(4,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×#63732 |
| Hall | C32×C5 ⋊ C4⋊C8 |
| Sylow | C32 ⋊ C5×C4⋊C8 |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3,4,5)(6,8)(7,10,11)(12,14,15,19,16,13,17,18);(6,7)(8,11)(9,10)(12,13,15,18,16,14,17,19)180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1877);