Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #90937 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Hall | C3×C5 ⋊ SD32 |
| Sylow | C5 ⋊ #828 |
| Sylow | C3 ⋊ #3959 |
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)(10,14)(11,18)(12,19)(15,16)(17,23)(20,24)(21,22);(2,3)(4,5)(6,7,8)(9,10,13,17)(11,14,20,23)(12,21,19,16)(15,24,22,18)Polycyclic presentation:
2^5,3,5|a^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,g^a=g^4,c^b=cd,d^b=de,f^b=f^248 conjugacy classes — view the full character table.
| maximal subgroup of | #11746823, #11746825, #11746842, … |
| maximal normal subgroup of | #11746823, #11746825, #11746842, … |
| maximal quotient of | #11745893, #11745897, #11745943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 17);