Finite Group DatabasebetaFinite Group Databasebeta| order | 6942 |
| isoclinism | isoclinic class of D89 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×D89 |
| unambiguous semidirect product | C89⋊(C2×C3×C13) |
| Fitting, socle, Hall | C3×C13×C89 ⋊ C2 |
| derived, Sylow | C89 ⋊ C2×C3×C13 |
| Hall | C13×C89 ⋊ C2×C3 |
| Hall | C3×C89 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D89 |
| commutator, hypocenter | C89 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C89 | C2 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C3×C13 | |
16 conjugacy classes of subgroups.
1794 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C13×#67063, C3×#17987775, C3×D13×D89, … |
| maximal normal subgroup of | C3×C13×#67063, C3×#17987775, C3×D13×D89, … |
| maximal quotient of | C3×C13×Dic89, C2×C3×C13×D89, C9×C13×D89, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6942, 3);