Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of D240 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D240 |
| Fitting | C3×C5×C16 ⋊ C2 |
| Hall | C3×C5 ⋊ D16 |
| Sylow | C5 ⋊ D48 |
| Sylow | C3 ⋊ D80 |
56 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19)(20,21,22,23,24);(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)(18,19)(21,24)(22,23)Polycyclic presentation:
2^5,3,5|b^2=cd,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,g^a=g^4123 conjugacy classes — view the full character table.
| maximal subgroup of | #11745819, #11745820, #11745824, … |
| maximal normal subgroup of | #11745819, #11745820, #11745824, … |
| maximal quotient of | D480, #11746270, Dic240, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 159);