Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | Aut(G) order 138240 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic360 |
| Hall | C5×C9 ⋊ Q32 |
| Sylow | C9 ⋊ Dic40 |
| Sylow | C5 ⋊ Dic72 |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 1440 |
A minimal faithful permutation representation — 2 generators on 46 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18)(33,34,35,36,37,38,39,40,41)(42,43,44,45,46);(1,17,9,25)(2,18,10,26)(3,19,11,27)(4,20,12,28)(5,21,13,29)(6,22,14,30)(7,23,15,31)(8,24,16,32)(34,41)(35,40)(36,39)(37,38)(43,46)(44,45)Polycyclic presentation:
2^5,3,5,3|a^2=e,b^2=cd,c^2=de,d^2=e,f^3=h,b^a=bc,c^a=cd,d^a=de,f^a=f^2h^2,g^a=g^4,h^a=h^2363 conjugacy classes — view the full character table.
| maximal subgroup of | Dic720, Dic1080, Dic1800, … |
| maximal normal subgroup of | Dic720 |
| maximal quotient of | Dic1080, Dic1800, Dic2520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 161);