Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #99 |
| Sylow | C5 ⋊ #806 |
| Sylow | C3 ⋊ #3966 |
104 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 34 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 — 2 generators on 16 points:
(1,2,4,5,3)(7,8)(9,11)(10,13)(12,16)(14,15);(2,3)(4,5)(6,7,8)(9,10)(11,15,16,13)(12,14)Polycyclic presentation:
2^5,3,5|a^2=c,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 | D5×#806, #11747128, #11747129, … |
| maximal normal subgroup of | D5×#806, #11747128, #11747129, … |
| maximal quotient of | #11745949, #11745952, #11745956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 72);