Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of (C2×D3)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Hall | C3×C5 ⋊ #117 |
| Sylow | C5 ⋊ #872 |
| Sylow | C3 ⋊ #4130 |
152 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 3 generators on 16 points:
(1,2,3,5,4)(6,7,8)(9,11,12,15)(10,14,13,16);(7,8)(10,13)(14,16);(2,3,4,5)(9,10)(11,14)(12,13)(15,16)Polycyclic presentation:
2^5,3,5|a^2=d,c^2=e,b^a=be,g^a=g^2,f^b=f^2,g^d=g^448 conjugacy classes — view the full character table.
| maximal subgroup of | #11751655, #11751656, #11751671, … |
| maximal normal subgroup of | #11751655, #11751656, #11751671, … |
| maximal quotient of | #11751745, #11751746, #11751747, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 985);