Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C1 |
| direct product | C5×#63357 |
| Fitting | C5×C9×C16 ⋊ C2 |
| Hall | C5×C9 ⋊ M32 |
| Sylow | C9 ⋊ C5×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)(6,11,13,12,7,9,8,14,10)(15,16,17,21,18,22,23,28,19,20,24,26,25,27,29,30);(7,9)(8,12)(10,11)(13,14)(16,20)(21,26)(22,27)(28,30)420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 117);