Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C5×D4 ⋊ C4 |
| Hall | C3×C5 ⋊ #104 |
| Sylow | C5 ⋊ #837 |
| Sylow | C3 ⋊ #4008 |
88 conjugacy classes of subgroups.
| 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)(9,11)(10,13)(12,15)(14,16);(2,3,4,5)(7,8)(9,10,12,14,13,11,16,15)Polycyclic presentation:
2^5,3,5|a^2=c,c^2=e,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 | #11751935, D3×#4008, #11751949, … |
| maximal normal subgroup of | #11751935, D3×#4008, #11751949, … |
| maximal quotient of | #11746740, #11746741, #11746743, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 313);