Finite Group DatabasebetaFinite Group Databasebeta| order | 8322 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C73⋊C3)⋊D19 |
| Fitting, socle, derived, Hall | C19×C73 ⋊ C2×C3 |
| Hall | C19×C73⋊C3 ⋊ C2 |
| Hall | D1387 ⋊ C3 |
| Hall | C73⋊C3 ⋊ D19 |
| Sylow | C73 ⋊ C3×D19 |
| Sylow | C19 ⋊ D73⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C73 | C2×C3 |
| LCS | G ▷ C19×C73 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,73|c^a=c^18,d^a=d^72,d^b=d^8261 conjugacy classes — view the full character table.
| maximal subgroup of | D19×D73⋊C3, C2×(C73⋊C3)⋊D19, #38735744, … |
| maximal normal subgroup of | D19×D73⋊C3, C2×(C73⋊C3)⋊D19, #38735744, … |
| maximal quotient of | #30659112, C2×(C73⋊C3)⋊D19, #10620321⋊D19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8322, 21);