Finite Group DatabasebetaFinite Group Databasebeta| order | 26166 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C89 · Schur multiplier (H2) = C7 |
| direct product | C89×C3⋊(C7⋊D7) |
| unambiguous semidirect product | C3⋊(C89×C7⋊D7) |
| unambiguous semidirect product | C7⋊(D21×C89) |
| Fitting, socle, Hall | C3×C72×C89 ⋊ C2 |
| derived, Hall | C3×C72 ⋊ C2×C89 |
| Hall | C72×C89 ⋊ D3 |
| Hall | C3×C89 ⋊ C7⋊D7 |
| Sylow | C72 ⋊ D3×C89 |
| Sylow | C3 ⋊ C89×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C89 | C3⋊(C7⋊D7) |
| commutator, cosocle, hypocenter | C3×C72 | C2×C89 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C89 | C2 |
| LCS | G ▷ C3×C72 | |
| UCS | C1 ◁ C89 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13083 |
6675 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26166, 45);