Finite Group DatabasebetaFinite Group Databasebeta| order | 26026 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C169 · Schur multiplier (H2) = C1 |
| direct product | D77×C169 |
| unambiguous semidirect product | C7⋊(D11×C169) |
| unambiguous semidirect product | C11⋊(D7×C169) |
| Fitting, Hall | C7×C11×C169 ⋊ C2 |
| derived, Hall | C7×C11 ⋊ C2×C169 |
| Hall | C11×C169 ⋊ D7 |
| Hall | C7×C169 ⋊ D11 |
| Sylow | C11 ⋊ D7×C169 |
| Sylow | C7 ⋊ D11×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | D77 |
| commutator, hypocenter | C7×C11 | C2×C169 |
| Frattini | C13 | C13×D77 |
| Fitting | C7×C11×C169 | C2 |
| socle, cosocle | C7×C11×C13 | C2×C13 |
| prime radical | C13×D77 | C13 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C169 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13013 |
6760 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26026, 7);