Finite Group DatabasebetaFinite Group Databasebeta| order | 1026 |
| isoclinism | isoclinic class of AGL(1,𝔽19) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #10587020⋊C2 |
| derived, Sylow | C19 ⋊ C2×C27 |
| Hall | #10587020 ⋊ C2 |
| Hall | D19 ⋊ C27 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | AGL(1,𝔽19) |
| commutator, hypocenter | C19 | C2×C27 |
| Fitting, socle | C3×C19 | C2×C9 |
| prime radical | C3×D19 | C9 |
| cosocle | #4294 | C2×C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
2,3^3,19|b^3=c,c^3=d,e^a=e^18,e^b=e^4,e^c=e^757 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1026, 7);