Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#63375 |
| Hall | C5×C9 ⋊ #97 |
| Sylow | C9 ⋊ C5×#97 |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 1440 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,2,3,4,5)(6,11,13,12,7,9,8,14,10)(19,20,21,24,22,23,25,26);(7,9)(8,12)(10,11)(13,14)(15,16,17,18)(20,23)(24,26)420 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 135);