Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C3×#685 |
| Fitting | C22×C3×C4×C5 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×C22⋊C4 |
| Sylow | C5 ⋊ C2×C3×C22⋊C4 |
264 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 18 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 18 points:
(3,4,5)(7,9)(10,11,12,13)(14,15,17,18,16);(6,7)(8,9)(15,16)(17,18);(1,2)156 conjugacy classes — view the full character table.
| maximal subgroup of | #11745948, C3×#64688, C3×#64915, … |
| maximal normal subgroup of | #11745948, C3×#64688, C3×#64915, … |
| maximal quotient of | C2×C3×#3937, C3×#65218, C3×C4×#685, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 720);