Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #124 |
| Sylow | C5 ⋊ #936 |
| Sylow | C3 ⋊ #4093 |
152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(6,7,8)(13,15,16,19)(14,17,18,20);(7,8)(10,12)(13,14,16,18)(15,20,19,17);(2,3)(4,5)(9,10)(11,12)(15,19)(17,20)Polycyclic presentation:
2^5,3,5|b^2=e,c^2=e,b^a=bd,c^a=ce,g^a=g^4,c^b=ce,f^b=f^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11746556, #11747381, #11747382, … |
| maximal normal subgroup of | #11746556, #11747381, #11747382, … |
| maximal quotient of | #11746895, #11746896, #11746897, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 444);