Finite Group DatabasebetaFinite Group Databasebeta| order | 7446 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C17⋊(D73⋊C3) |
| unambiguous semidirect product | (C73⋊C3)⋊D17 |
| unambiguous semidirect product | D1241⋊C3 |
| Fitting, socle, derived, Hall | C17×C73 ⋊ C2×C3 |
| Hall | C17×C73⋊C3 ⋊ C2 |
| Hall | D1241 ⋊ C3 |
| Hall | C73⋊C3 ⋊ D17 |
| Sylow | C73 ⋊ C3×D17 |
| Sylow | C17 ⋊ D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C73 | C2×C3 |
| LCS | G ▷ C17×C73 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,17,73|c^a=c^16,d^a=d^72,d^b=d^8234 conjugacy classes — view the full character table.
| maximal subgroup of | #19097218⋊C3, #19097219⋊C3, D17×D73⋊C3, … |
| maximal normal subgroup of | #19097218⋊C3, #19097219⋊C3, D17×D73⋊C3, … |
| maximal quotient of | Dic1241⋊C3, C2×C17⋊(D73⋊C3), C17⋊(#10620321⋊C2), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7446, 12);