Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ #102 |
| Sylow | C5 ⋊ #821 |
| Sylow | C3 ⋊ #4007 |
100 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 30 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:
(1,2,3,5,4)(7,8)(10,14)(11,12)(15,16);(2,3,4,5)(6,7,8)(9,10,11,14,13,16,12,15)Polycyclic presentation:
2^5,3,5|a^2=c,c^2=e,d^2=e,b^a=bd,g^a=g^2,c^b=ce,d^b=de,f^b=f^2,g^c=g^439 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#204, AGL(1,𝔽5)×D24, #11751661, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#204, AGL(1,𝔽5)×D24, #11751661, … |
| maximal quotient of | #11746457, #11746459, #11746462, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 228);