Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C4×C5×#67 |
| Fitting | C22×C3×C4×C5 ⋊ C2 |
| Hall | C3×C5 ⋊ C4×D4 |
| Sylow | C3 ⋊ C4×C5×D4 |
188 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 90 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)(12,13,14,15,16);(2,3)(8,9)(10,11);(4,5,6,7)180 conjugacy classes — view the full character table.
| maximal subgroup of | #11748314, #67×#168, #11748484, … |
| maximal normal subgroup of | #11748314, #67×#168, #11748484, … |
| maximal quotient of | C4×C5×Dic3⋊C4, C5×#4933, C4×C5×(C2×D3)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 807);