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) = C22 |
| unambiguous semidirect product | D5⋊ΓL(1,𝔽25) |
| Hall | C3×C5 ⋊ C2×M16 |
| Sylow | C5 ⋊ C2×ΓL(1,𝔽25) |
| Sylow | C3 ⋊ D5⋊M16 |
136 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 136 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)(9,11,13,12)(10,15,14,16);(7,8)(10,14)(15,16);(2,3,4,5)(9,10,12,16,13,14,11,15)Polycyclic presentation:
2^5,3,5|a^2=d,c^2=e,d^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 | AGL(1,𝔽5)×ΓL(1,𝔽25), #11751650, #11751655, … |
| maximal normal subgroup of | AGL(1,𝔽5)×ΓL(1,𝔽25), #11751650, #11751655, … |
| maximal quotient of | #11751785, #11751786, #11751787, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 993);