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 ⋊ #885 |
| Sylow | C3 ⋊ #4031 |
152 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 46 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)(9,10,11,12)(14,18)(15,20);(7,8)(10,12)(13,15)(14,17)(16,20)(18,19);(2,3)(4,5)(10,12)(13,14)(15,19)(16,18)(17,20)Polycyclic presentation:
2^5,3,5|c^2=de,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 | #11752553, #11752555, #11752584, … |
| maximal normal subgroup of | #11752553, #11752555, #11752584, … |
| maximal quotient of | #11747975, #11747976, #11747978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 540);