Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of (C2×D3)⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D3)⋊#170 |
| Hall | C3×C5 ⋊ C22⋊C8 |
| Sylow | C5 ⋊ (C2×D3)⋊C8 |
| Sylow | C3 ⋊ C22⋊#170 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 20 points:
(1,2,3,5,4)(7,8)(10,12);(2,3,4,5)(6,7,8)(9,10)(11,12)(13,14,15,17,16,18,19,20)Polycyclic presentation:
2^5,3,5|a^2=c,c^2=e,b^a=bd,g^a=g^2,f^b=f^2,g^c=g^448 conjugacy classes — view the full character table.
| maximal subgroup of | #11751754, #11751772, #11751773, … |
| maximal normal subgroup of | #11751754, #11751772, #11751773, … |
| maximal quotient of | #11746488, #11746489, #11746492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 246);