Finite Group DatabasebetaFinite Group Databasebeta| order | 18018 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D33×#63270 |
| unambiguous semidirect product | C3⋊(D11×#63270) |
| unambiguous semidirect product | C11⋊(D3×#63270) |
| 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 |
594 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D33×#10587722, D33×#10587720, D33⋊#10587722, … |
| maximal normal subgroup of | D33×#10587722, D33×#10587720, D33⋊#10587722, … |
| maximal quotient of | Dic33×#63270, C2×D33×#63270 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18018, 111);