Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C42 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×#3947 |
| Hall | C32×C5 ⋊ #97 |
| Sylow | C5 ⋊ C32×#97 |
240 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 1440 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3)(7,8,10,11,9)(16,17,18,21,19,20,22,23);(4,5,6)(8,9)(10,11)(12,13,14,15)(17,20)(21,23)468 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1251);