Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C3⋊(D41⋊C25) |
| unambiguous semidirect product | (C2×C3)⋊(D41⋊C25) |
| unambiguous semidirect product | (C2×D123)⋊C25 |
| unambiguous semidirect product | (C2×C41⋊C25)⋊D3 |
| derived, Hall | C3×C41 ⋊ C22×C25 |
| Hall | C3×C41⋊C25 ⋊ C22 |
| Hall | C41⋊C25 ⋊ C2×D3 |
| Hall | C2×D123 ⋊ C25 |
| Sylow | C41 ⋊ C2×D3×C25 |
| Sylow | C3 ⋊ C2×D41⋊C25 |
60 conjugacy classes of subgroups.
270 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C9⋊(D41⋊C25), D3×C3⋊(D41⋊C25), C2×C3×C3⋊(D41⋊C25), … |
| maximal normal subgroup of | C2×C3×C3⋊(D41⋊C25) |
| maximal quotient of | C2×C9⋊(D41⋊C25), D3×C3⋊(D41⋊C25), C2×C3×C3⋊(D41⋊C25), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 19);