Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| isoclinism | isoclinic class of D9 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C169 · Schur multiplier (H2) = C1 |
| direct product | Dic9×C169 |
| unambiguous semidirect product | C9⋊(C4×C169) |
| derived, Sylow | C9 ⋊ C4×C169 |
| Hall | C9×C169 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C169 | D9 |
| commutator, hypocenter | C9 | C4×C169 |
| Frattini, socle | C2×C3×C13 | D3×C13 |
| Fitting | C2×C9×C169 | C2 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C2×C169 | |
27 conjugacy classes of subgroups.
2028 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×Dic9×C169, C169×Dic45, C169×C9⋊AGL(1,𝔽5) |
| maximal normal subgroup of | C5×Dic9×C169 |
| maximal quotient of | C5×Dic9×C169, C169×Dic45, C169×C9⋊AGL(1,𝔽5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 4);