Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C5×D4 ⋊ C4 |
| Hall | C3×C5 ⋊ #102 |
| Sylow | C5 ⋊ #832 |
| Sylow | C3 ⋊ #4007 |
100 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 33 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:
(1,2,5,3,4)(6,7,8)(10,13)(11,16)(14,15);(2,3,4,5)(7,8)(9,10)(11,13)(12,15)(14,16)Polycyclic presentation:
2^5,3,5|a^2=c,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^3,d^b=de,g^c=g^439 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#4007, #11751937, #11751938, … |
| maximal normal subgroup of | D3×#4007, #11751937, #11751938, … |
| maximal quotient of | #11746739, #11746742, #11746744, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 312);