Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #91222 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C3×C5×C8 ⋊ C4 |
| Hall | C3×C5 ⋊ #107 |
| Sylow | C5 ⋊ #818 |
| Sylow | C3 ⋊ #3994 |
72 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)(9,10,14,16,12,15,11,13);(2,3,4,5)(7,8)(10,13)(11,14)(15,16)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=de,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^3,g^c=g^454 conjugacy classes — view the full character table.
| maximal subgroup of | #11746457, #11746459, #11746476, … |
| maximal normal subgroup of | #11746457, #11746459, #11746476, … |
| maximal quotient of | #11746720, #11746721, #11746722, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 299);