Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×C22⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ #123 |
| Sylow | C5 ⋊ #886 |
| Sylow | C3 ⋊ #4032 |
156 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 55 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);(13,15)(14,17)(16,20)(18,19);(2,3)(4,5)(7,8)(10,12)(13,14)(15,19)(16,18)(17,20)Polycyclic presentation:
2^5,3,5|c^2=de,b^a=be,c^a=cd,f^a=f^2,g^a=g^4,c^b=ce84 conjugacy classes — view the full character table.
| maximal subgroup of | #11747136, #11750843, #11752813, … |
| maximal normal subgroup of | #11747136, #11750843, #11752813, … |
| maximal quotient of | #11750754, #11750760, #11750762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 851);