Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ AGL(1,ℤ/8) |
| Sylow | C5 ⋊ #932 |
| Sylow | C3 ⋊ #4054 |
136 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 44 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)(10,14)(13,16);(7,8)(9,10,11,13,12,14,15,16);(2,3)(4,5)(10,13)(11,15)(14,16)Polycyclic presentation:
2^5,3,5|b^2=d,d^2=e,b^a=bd,d^a=de,g^a=g^4,c^b=ce,f^b=f^257 conjugacy classes — view the full character table.
| maximal subgroup of | #11747114, #11747121, #11748087, … |
| maximal normal subgroup of | #11747114, #11747121, #11748087, … |
| maximal quotient of | #11746888, #11746892, #11746917, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 388);