Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #91159 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C3×C5 ⋊ #106 |
| Sylow | C5 ⋊ #808 |
| Sylow | C3 ⋊ #3993 |
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:
(1,2,3,5,4)(7,8)(9,10,11,13,12,14,15,16);(2,3,4,5)(6,7,8)(10,13)(11,15)(14,16)Polycyclic presentation:
2^5,3,5|a^2=c,b^2=d,d^2=e,b^a=bd,d^a=de,g^a=g^2,f^b=f^2,g^c=g^436 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3993, #11751653, #11751654, … |
| maximal normal subgroup of | D3×#3993, #11751653, #11751654, … |
| maximal quotient of | #11746472, #11746473, #11746474, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 235);