Finite Group DatabasebetaFinite Group Databasebeta| order | 18810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊(#4294⋊C2) |
| unambiguous semidirect product | #4294⋊AGL(1,𝔽11) |
| unambiguous semidirect product | (C11⋊(#4294⋊C2))⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C11⋊C5)⋊(D19⋊C3) |
| commutator, hypocenter | C11×C19 | C2×C5×C9 |
| Fitting, socle, cosocle | C3×C11×C19 | C2×C3×C5 |
| prime radical | C3×C19⋊AGL(1,𝔽11) | C3 |
| LCS | G ▷ C11×C19 | |
| UCS | C1 ◁ C3 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1881 |
Polycyclic presentation:
2,3,5,11,19,3|b^3=f,d^a=d^10,e^a=e^18,e^b=e^7,d^c=d^4162 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽11)×#4294⋊C2, C2×(C11⋊C5)⋊(#4294⋊C2) |
| maximal normal subgroup of | AGL(1,𝔽11)×#4294⋊C2, C2×(C11⋊C5)⋊(#4294⋊C2) |
| maximal quotient of | (C11⋊C5)⋊(#4294⋊C4), C2×(C11⋊C5)⋊(#4294⋊C2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18810, 36);