Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#3930 |
| Fitting | C5×C9×C16 ⋊ C2 |
| Hall | C5×C9 ⋊ M32 |
| Sylow | C5 ⋊ C9×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:
(1,2,3,4,5,6,7,8,9)(10,11,13,14,12)(15,16,17,21,18,22,23,28,19,20,24,26,25,27,29,30);(11,12)(13,14)(16,20)(21,26)(22,27)(28,30)468 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 76);