Finite Group DatabasebetaFinite Group Databasebeta| order | 6084 |
| isoclinism | isoclinic class of D169 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×C9×D169 |
| Fitting | C2×C9×C169 ⋊ C2 |
| derived, Sylow | C169 ⋊ C22×C9 |
| Hall | C9×C169 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C9 | D169 |
| commutator, hypocenter | C169 | C22×C9 |
| Frattini | C3×C13 | C2×C3×D13 |
| Fitting | C2×C9×C169 | C2 |
| socle | C2×C3×C13 | C3×D13 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C2×C9 | |
45 conjugacy classes of subgroups.
1548 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×D5×D169, C2×C5×C9×D169, C2×C9×D845 |
| maximal normal subgroup of | C2×C5×C9×D169 |
| maximal quotient of | C9×D5×D169, C2×C5×C9×D169, C2×C9×D845 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6084, 16);