Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×D3×#168 |
| derived | C3×C5 ⋊ C2×C5×C8 |
| Hall | C3×C52 ⋊ C2×C8 |
| Sylow | C52 ⋊ D3×C8 |
| Sylow | C3 ⋊ C2×C5×#168 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#87767, C5×D3×#681, D3×#87769, … |
| maximal normal subgroup of | D3×#87767, C5×D3×#681, D3×#87769, … |
| maximal quotient of | C5×#10623818, C2×C5×D3×#168 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 285);