Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #90938 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ SD32 |
| Sylow | C5 ⋊ #828 |
| Sylow | C3 ⋊ #3932 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 24 points:
(1,2,4,5,3)(7,8)(9,11,17,16,23,20,12,15,14,19,24,10,13,18,21,22);(2,3)(4,5)(6,7,8)(9,10,14,16)(11,17,19,24)(12,20,21,18)(13,22,23,15)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=cd,c^2=d,d^2=e,b^a=bc,c^a=cde,d^a=de,g^a=g^4,f^b=f^266 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3932, #11746821, #11746830, … |
| maximal normal subgroup of | D3×#3932, #11746821, #11746830, … |
| maximal quotient of | #11745895, #11745898, #11745944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 19);