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 ⋊ #908 |
| Sylow | C3 ⋊ #4095 |
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)(9,11,13,12)(10,14,15,16);(7,8)(9,10)(11,14)(12,16)(13,15);(2,3)(4,5)(9,10,12,14,13,15,11,16)Polycyclic presentation:
2^5,3,5|a^2=d,c^2=e,d^2=e,b^a=bd,c^a=ce,g^a=g^4,d^b=de,f^b=f^257 conjugacy classes — view the full character table.
| maximal subgroup of | #11747118, #11747125, #11748085, … |
| maximal normal subgroup of | #11747118, #11747125, #11748085, … |
| maximal quotient of | #11746883, #11746899, #11746909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 381);