Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Hall | C3×C5 ⋊ C4×Q8 |
| Sylow | C5 ⋊ #887 |
| Sylow | C3 ⋊ #4033 |
140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 3 generators on 20 points:
(1,2,4,5,3)(6,7,8)(9,11,12,10)(15,19)(17,20);(13,15,16,19)(14,17,18,20);(2,3)(4,5)(7,8)(9,10,12,11)(13,14,16,18)(15,17,19,20)Polycyclic presentation:
2^5,3,5|a^2=e,b^2=d,c^2=de,f^a=f^2,g^a=g^4,c^b=cd90 conjugacy classes — view the full character table.
| maximal subgroup of | #11747181, #11747182, #11747184, … |
| maximal normal subgroup of | #11747181, #11747182, #11747184, … |
| maximal quotient of | #11750747, #11750750, #11750753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 852);