Finite Group DatabasebetaFinite Group Databasebeta| order | 26166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C89 · Schur multiplier (H2) = C1 |
| direct product | C89×D49⋊C3 |
| unambiguous semidirect product | D49⋊(C3×C89) |
| unambiguous semidirect product | (C49⋊C3)⋊(C2×C89) |
| unambiguous semidirect product | (C89×D49)⋊C3 |
| Fitting, Hall | C49×C89 ⋊ C2×C3 |
| derived, Sylow | C49 ⋊ C2×C3×C89 |
| Hall | C89×C49⋊C3 ⋊ C2 |
| Hall | C89×D49 ⋊ C3 |
| Hall | C49⋊C3 ⋊ C2×C89 |
| Hall | D49 ⋊ C3×C89 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | D49⋊C3 |
| commutator, cosocle, hypocenter | C49 | C2×C3×C89 |
| Frattini | C7 | AGL(1,𝔽7)×C89 |
| Fitting | C49×C89 | C2×C3 |
| socle | C7×C89 | AGL(1,𝔽7) |
| LCS | G ▷ C49 | |
| UCS | C1 ◁ C89 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4361 |
1246 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26166, 11);