Finite Group DatabasebetaFinite Group Databasebeta| order | 26862 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C121 · Schur multiplier (H2) = C1 |
| direct product | C121×D37⋊C3 |
| unambiguous semidirect product | D37⋊(C3×C121) |
| unambiguous semidirect product | (C37⋊C3)⋊(C2×C121) |
| unambiguous semidirect product | (D37×C121)⋊C3 |
| Fitting, Hall | C37×C121 ⋊ C2×C3 |
| derived, Sylow | C37 ⋊ C2×C3×C121 |
| Hall | C37⋊C3×C121 ⋊ C2 |
| Hall | D37×C121 ⋊ C3 |
| Hall | C37⋊C3 ⋊ C2×C121 |
| Hall | D37 ⋊ C3×C121 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C121 | D37⋊C3 |
| commutator, hypocenter | C37 | C2×C3×C121 |
| Frattini | C11 | C11×D37⋊C3 |
| Fitting | C37×C121 | C2×C3 |
| socle, cosocle | C11×C37 | C2×C3×C11 |
| prime radical | C11×D37⋊C3 | C11 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C121 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4477 |
1452 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26862, 10);