Finite Group DatabasebetaFinite Group Databasebeta| order | 15675 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C11×C25 · Schur multiplier (H2) = C1 |
| direct product | C11×C25×C19⋊C3 |
| unambiguous semidirect product | C19⋊(C3×C11×C25) |
| unambiguous semidirect product | (C19×C25)⋊(C3×C11) |
| unambiguous semidirect product | (C11×C19×C25)⋊C3 |
| Fitting, Hall | C11×C19×C25 ⋊ C3 |
| derived, Sylow | C19 ⋊ C3×C11×C25 |
| Hall | C19×C25 ⋊ C3×C11 |
| Hall | C11×C19 ⋊ C3×C25 |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5225 |
2475 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C11×C25×C19⋊C3, C11×C25×D19⋊C3, D11×C25×C19⋊C3, … |
| maximal normal subgroup of | C2×C11×C25×C19⋊C3, C11×C25×D19⋊C3, D11×C25×C19⋊C3, … |
| maximal quotient of | C2×C11×C25×C19⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15675, 3);