Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C3×C4×C5 ⋊ C4 |
| Hall | C3×C5 ⋊ #99 |
| Sylow | C5 ⋊ #834 |
| Sylow | C3 ⋊ #3999 |
104 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)(9,11,12,16)(10,13,14,15);(2,3,4,5)(7,8)(9,10)(11,15,16,13)(12,14)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^3,c^b=ce,g^c=g^445 conjugacy classes — view the full character table.
| maximal subgroup of | #11746554, #11746555, #11746556, … |
| maximal normal subgroup of | #11746554, #11746555, #11746556, … |
| maximal quotient of | #11746724, #11746725, #11746726, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 304);