Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | Dic5×#67 |
| Hall | C3×C5 ⋊ C4×D4 |
| Sylow | C5 ⋊ C4×#67 |
| Sylow | C3 ⋊ D4×Dic5 |
188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 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:
(1,2,3)(9,11)(12,13,15,16,14);(2,3)(8,9)(10,11);(4,5,6,7)(13,14)(15,16)72 conjugacy classes — view the full character table.
| maximal subgroup of | #11751992, #67×#170, #67⋊#170, … |
| maximal normal subgroup of | #11751992, #67×#170, #67⋊#170, … |
| maximal quotient of | #67×#168, #11748484, #11748500, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 627);