Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #63734 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#63735 |
| Hall | C32×C5 ⋊ SD32 |
| Sylow | C32 ⋊ C5×SD32 |
92 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5)(6,8)(7,10,11)(12,13,16,19)(14,21,23,27)(15,24,22,18)(17,25,26,20);(6,7)(8,11)(9,10)(13,17)(14,20)(15,22)(18,27)(19,26)(21,24)(23,25)105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1880);