Finite Group DatabasebetaFinite Group Databasebeta| order | 26166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C49 · Schur multiplier (H2) = C1 |
| direct product | C3×C49×D89 |
| unambiguous semidirect product | C89⋊(C2×C3×C49) |
| Fitting, Hall | C3×C49×C89 ⋊ C2 |
| derived, Sylow | C89 ⋊ C2×C3×C49 |
| Hall | C49×C89 ⋊ C2×C3 |
| Hall | C3×C89 ⋊ C2×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C49 | D89 |
| commutator, hypocenter | C89 | C2×C3×C49 |
| Frattini | C7 | C3×C7×D89 |
| Fitting | C3×C49×C89 | C2 |
| socle | C3×C7×C89 | C2×C7 |
| prime radical | C3×C7×D89 | C7 |
| cosocle | C7×C89 | C2×C3×C7 |
| LCS | G ▷ C89 | |
| UCS | C1 ◁ C3×C49 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13083 |
6762 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26166, 3);