Finite Group DatabasebetaFinite Group Databasebeta| order | 480 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×C3×#709 |
| Fitting | C22×C3×C4×C5 ⋊ C2 |
| Hall | C3×C5 ⋊ C2×#41 |
| Sylow | C5 ⋊ C2×C3×#41 |
328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 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 — 4 generators on 18 points:
(1,2)(3,4,5)(6,7,9,10,8)(12,16)(15,18);(11,13,14,17)(12,15,16,18);(7,8)(9,10)(11,12)(13,15)(14,16)(17,18);(1,2)156 conjugacy classes — view the full character table.
| maximal subgroup of | #11748342, #11748343, #11748353, … |
| maximal normal subgroup of | #11748342, #11748343, #11748353, … |
| maximal quotient of | C2×C3×C4×Dic10, C2×C3×#4016, C3×#65804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(480, 1138);