Finite Group DatabasebetaFinite Group Databasebeta| order | 18018 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C11⋊#10587716) |
| unambiguous semidirect product | C11⋊(C3⋊#10587716) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C11×C13 | C2×C3 |
| LCS | G ▷ C3×C7×C11×C13 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3003 |
Polycyclic presentation:
2,3^2,7,11,13|c^a=c^2,e^a=e^10,f^a=f^12,d^b=d^2,f^b=f^3552 conjugacy classes — view the full character table.
| maximal subgroup of | #10587720⋊D33, #10587722⋊D33, #49114749, … |
| maximal normal subgroup of | #10587720⋊D33, #10587722⋊D33, #49114749, … |
| maximal quotient of | C3⋊(C11⋊#11763957), C2×C3⋊(C11⋊#10587716) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18018, 109);