Finite Group DatabasebetaFinite Group Databasebeta| order | 12300 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25×C41 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C25×C41 |
| unambiguous semidirect product | C3⋊(C4×C25×C41) |
| derived, Sylow | C3 ⋊ C4×C25×C41 |
| Hall | C3×C25×C41 ⋊ C4 |
| Hall | C3×C41 ⋊ C4×C25 |
| Hall | C3×C25 ⋊ C4×C41 |
36 conjugacy classes of subgroups.
6150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×Dic9×C41, C3×Dic3×C25×C41, C25×C3⋊Dic3×C41 |
| maximal normal subgroup of | C3×Dic3×C25×C41 |
| maximal quotient of | C25×Dic9×C41, C3×Dic3×C25×C41, C25×C3⋊Dic3×C41 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12300, 9);