Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #63734 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#63734 |
| Hall | C32×C5 ⋊ D16 |
| Sylow | C32 ⋊ C5×D16 |
100 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)(13,17)(14,21)(15,22)(18,19)(20,26)(23,27)(24,25);(6,7)(8,11)(9,10)(12,13)(14,17)(15,24)(16,20)(18,21)(19,22)(23,26)(25,27)105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1879);