Finite Group DatabasebetaFinite Group Databasebeta| order | 26166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽8)×D623 |
| unambiguous semidirect product | C89⋊(D7×ΓL(1,𝔽8)) |
| Fitting, socle, derived, Hall | C72×C89 ⋊ C2×C3 |
| Hall | C7×ΓL(1,𝔽8)×C89 ⋊ C2 |
| Hall | C7×D623 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ D89 |
| Sylow | C89 ⋊ D7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ C3×D89 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C72×C89 | C2×C3 |
| LCS | G ▷ C72×C89 | |
| UCS | C1 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3738 |
1565 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26166, 22);