Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #123 |
| Sylow | C5 ⋊ #935 |
| Sylow | C3 ⋊ #4040 |
156 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(10,12)(13,16,17,15)(14,18,19,20);(7,8)(9,10)(11,12)(13,15,17,16)(14,18,19,20);(2,3)(4,5)(13,14)(15,18)(16,20)(17,19)Polycyclic presentation:
2^5,3,5|b^2=d,c^2=d,c^a=cd,g^a=g^4,c^b=ce,f^b=f^260 conjugacy classes — view the full character table.
| maximal subgroup of | #11752563, #11752564, #11752566, … |
| maximal normal subgroup of | #11752563, #11752564, #11752566, … |
| maximal quotient of | #11747192, #11747193, #11747194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 483);