Finite Group DatabasebetaFinite Group Databasebeta| order | 1800 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2 |
| direct product | C3×C5×D3×Dic5 |
| derived | C3×C5 ⋊ C2×C3×C4×C5 |
| Hall | C32×C52 ⋊ C2×C4 |
| Sylow | C52 ⋊ C3×C4×D3 |
| Sylow | C32 ⋊ C2×C5×Dic5 |
184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 184 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.
| transitive degree | μt(G) = 120 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D3×#6036, C3×C5×D3×C22⋊D5, C3×D3×#6038, … |
| maximal normal subgroup of | C3×D3×#6036, C3×C5×D3×C22⋊D5, C3×D3×#6038 |
| maximal quotient of | C5×Dic5×AGL(1,ℤ/9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1800, 415);