Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×A4⋊Q8 |
| unambiguous semidirect product | A4⋊(C5×Q8) |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 120 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2,4)(5,7,8,12)(6,9,10,11)(13,14,15,16,17);(2,3)(5,6,8,10)(7,11,12,9)70 conjugacy classes — view the full character table.
| maximal subgroup of | #11751574, #11751576, #11751581, … |
| maximal normal subgroup of | #11751574, #11751576, #11751581, … |
| maximal quotient of | C5×#5386, C5×#5389, C5×#5391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1013);