Finite Group DatabasebetaFinite Group Databasebeta| order | 18810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C11⋊C5×AGL(1,𝔽19) |
| unambiguous semidirect product | #4296⋊(C2×C11⋊C5) |
| unambiguous semidirect product | (C11×AGL(1,𝔽19))⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C19 | C2×C5×C9 |
| prime radical | C11⋊C5×D19⋊C3 | C3 |
| cosocle | C11×C19⋊C3 | C2×C3×C5 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 209 |
133 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×AGL(1,𝔽19), C2×C11⋊C5×AGL(1,𝔽19) |
| maximal normal subgroup of | AGL(1,𝔽11)×AGL(1,𝔽19), C2×C11⋊C5×AGL(1,𝔽19) |
| maximal quotient of | C11⋊C5×#4296⋊C4, C2×C11⋊C5×AGL(1,𝔽19) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18810, 40);