Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C5×C8 ⋊ C22 |
| Hall | C3×C5 ⋊ C2×D8 |
| Sylow | C5 ⋊ D3×D8 |
| Sylow | C3 ⋊ D5×D8 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,4,5,3)(6,7,8)(9,10,14,16,12,15,11,13);(7,8)(10,13)(11,14)(15,16);(2,3)(4,5)(10,13)(11,14)(15,16)Polycyclic presentation:
2^5,3,5|c^2=de,d^2=e,c^a=cd,d^a=de,g^a=g^4,c^b=cd,d^b=de,f^b=f^251 conjugacy classes — view the full character table.
| maximal subgroup of | #11746822, #11746823, #11746824, … |
| maximal normal subgroup of | #11746822, #11746823, #11746824, … |
| maximal quotient of | #11746822, #11746823, #11746824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 332);