Finite Group DatabasebetaFinite Group Databasebeta| order | 9996 |
| isoclinism | isoclinic class of D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C49 · Schur multiplier (H2) = C2 |
| direct product | C2×C49×D51 |
| unambiguous semidirect product | (C2×C3)⋊(D17×C49) |
| unambiguous semidirect product | (C2×C17)⋊(D3×C49) |
| Fitting | C2×C3×C17×C49 ⋊ C2 |
| derived, Hall | C3×C17 ⋊ C22×C49 |
| Hall | C3×C17×C49 ⋊ C22 |
| Hall | C17×C49 ⋊ C2×D3 |
| Hall | C3×C49 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D3×C49 |
| Sylow | C3 ⋊ C2×D17×C49 |
60 conjugacy classes of subgroups.
2646 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C49×D153, C2×D51×C49⋊C3, D3×C49×D51, … |
| maximal normal subgroup of | C2×D51×C49⋊C3, C2×C3×C49×D51 |
| maximal quotient of | C2×C49×D153, D3×C49×D51, C2×C49×C3⋊D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9996, 38);