Finite Group DatabasebetaFinite Group Databasebeta| order | 1200 |
| isoclinism | isoclinic class of D3×D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C4×C5×D3×D5 |
| Fitting | C3×C4×C52 ⋊ C22 |
| derived | C3×C5 ⋊ C22×C4×C5 |
| Hall | C3×C52 ⋊ C22×C4 |
| Sylow | C52 ⋊ C2×C4×D3 |
| Sylow | C3 ⋊ C2×C4×C5×D5 |
248 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×D52, C5×D3×#709, D3×#87873, … |
| maximal normal subgroup of | C4×D3×D52, C5×D3×#709, D3×#87873, … |
| maximal quotient of | C5×D3×#685 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1200, 786);