Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×Q8 ⋊ C22 |
| Hall | C3×C5 ⋊ AGL(1,ℤ/8) |
| Sylow | C5 ⋊ #949 |
| Sylow | C3 ⋊ #4060 |
136 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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)(9,10,12,13)(11,16,15,14);(7,8)(10,14)(11,15)(13,16);(2,3)(4,5)(10,13)(14,16)Polycyclic presentation:
2^5,3,5|c^2=e,d^2=e,c^a=ce,g^a=g^4,c^b=cd,d^b=de,f^b=f^2,d^c=de45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4060, #11754067, #11754092, … |
| maximal normal subgroup of | D3×#4060, #11754067, #11754092, … |
| maximal quotient of | #11747155, #11747167, #11747189, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 578);