Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of D123 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×C25×D123 |
| unambiguous semidirect product | (C2×C3)⋊(C25×D41) |
| Fitting | C2×C3×C25×C41 ⋊ C2 |
| derived, Hall | C3×C41 ⋊ C22×C25 |
| Hall | C3×C25×C41 ⋊ C22 |
| Hall | C25×C41 ⋊ C2×D3 |
| Hall | C3×C25 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×D3×C25 |
| Sylow | C3 ⋊ C2×C25×D41 |
60 conjugacy classes of subgroups.
3150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C25×D369, D3×C25×D123, C2×C25×C3⋊D123, … |
| maximal normal subgroup of | C2×C3×C25×D123 |
| maximal quotient of | C2×C25×D369, D3×C25×D123, C2×C25×C3⋊D123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 44);