Finite Group DatabasebetaFinite Group Databasebeta| order | 18810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D55×#4296 |
| unambiguous semidirect product | C5⋊(D11×#4296) |
| unambiguous semidirect product | C11⋊(D5×#4296) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C11×C19 | C2×C9 |
| prime radical | C19⋊C3×D55 | C3 |
| cosocle | C5×C11×C19⋊C3 | C2×C3 |
| LCS | G ▷ C5×C11×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1045 |
319 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D55×AGL(1,𝔽19), D55⋊AGL(1,𝔽19), D5×D11×#4296, … |
| maximal normal subgroup of | D55×AGL(1,𝔽19), D55⋊AGL(1,𝔽19), D5×D11×#4296, … |
| maximal quotient of | #4296×Dic55, C2×D55×#4296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18810, 55);