Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | M16×D15 |
| Fitting | C3×C5×M16 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×M16 |
| Sylow | C5 ⋊ D3×M16 |
| Sylow | C3 ⋊ D5×M16 |
136 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 57 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:
(2,3)(4,5)(7,8);(1,2,4,5,3)(6,7,8)(10,13)(14,16);(9,10,11,14,12,13,15,16)90 conjugacy classes — view the full character table.
| maximal subgroup of | #11748170, #11748173, #11748224, … |
| maximal normal subgroup of | #11748170, #11748173, #11748224, … |
| maximal quotient of | #11750802, D15×#97, #11750806, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 871);