Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×D5×C4⋊C4 |
| Fitting | C3×C5×C4⋊C4 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×C4⋊C4 |
| Sylow | C5 ⋊ C2×C3×C4⋊C4 |
184 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 98 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:
(5,8,7,6)(9,10,12,13,11)(14,15,16);(1,4,3,2)(6,8);(10,11)(12,13)120 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#64874, #11746745, #11747164, … |
| maximal normal subgroup of | C3×#64874, #11746745, #11747164, … |
| maximal quotient of | C3×#64936, C3×#64938, C3×#64939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 684);