Finite Group DatabasebetaFinite Group Databasebeta| order | 26106 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊D229 |
| Fitting, socle, derived, Hall | C19×C229 ⋊ C2×C3 |
| Hall | C19⋊C3×C229 ⋊ C2 |
| Hall | D4351 ⋊ C3 |
| Sylow | C229 ⋊ D19⋊C3 |
| Hall | C19⋊C3 ⋊ D229 |
| Sylow | C19 ⋊ C3×D229 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C19×C229 | C2×C3 |
| LCS | G ▷ C19×C229 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,19,229|c^a=c^18,d^a=d^228,c^b=c^71035 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26106, 27);