Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D169⋊C9 |
| unambiguous semidirect product | D169⋊(C2×C9) |
| unambiguous semidirect product | (C2×D169)⋊C9 |
| unambiguous semidirect product | (C169⋊C9)⋊C22 |
| unambiguous semidirect product | (C2×C169⋊C9)⋊C2 |
| derived, Sylow | C169 ⋊ C22×C9 |
| Hall | C169⋊C9 ⋊ C22 |
| Hall | C2×D169 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3 | D169⋊C3 |
| commutator, hypocenter | C169 | C22×C9 |
| Frattini | C3×C13 | C2×D13⋊C3 |
| Fitting | C2×C3×C169 | C2×C3 |
| socle | C2×C3×C13 | D13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C2×C3 | |
45 conjugacy classes of subgroups.
204 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D169⋊C9, C2×C5×D169⋊C9, C2×C5⋊(D169⋊C9) |
| maximal normal subgroup of | C2×C5×D169⋊C9 |
| maximal quotient of | D5×D169⋊C9, C2×C5×D169⋊C9, C2×C5⋊(D169⋊C9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 9);