Finite Group DatabasebetaFinite Group Databasebeta| order | 26106 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D229⋊C3 |
| Fitting, socle, Hall | C19×C229 ⋊ C2×C3 |
| derived, Sylow | C229 ⋊ C2×C3×C19 |
| Hall | C19×C229⋊C3 ⋊ C2 |
| Hall | C19×D229 ⋊ C3 |
| Hall | C229⋊C3 ⋊ C2×C19 |
| Hall | D229 ⋊ C3×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D229⋊C3 |
| commutator, cosocle, hypocenter | C229 | C2×C3×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C229 | C2×C3 |
| LCS | G ▷ C229 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
836 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26106, 18);