Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of #1201 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×#1202 |
| Hall | C3×C5 ⋊ C4×D4 |
| Sylow | C5 ⋊ C4×#67 |
| Sylow | C3 ⋊ C4×D20 |
188 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 240 |
A minimal faithful permutation representation — 3 generators on 16 points:
(1,2,4,5,3)(7,8)(13,14,15,16);(2,3)(4,5)(6,7,8)(14,16);(9,10,11,12)84 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#1202, #11747698, #11747705, … |
| maximal normal subgroup of | C8×#1202, #11747698, #11747705, … |
| maximal quotient of | C4×#6653, #11747023, C4×#6657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 519);