Finite Group DatabasebetaFinite Group Databasebeta| order | 18018 |
| isoclinism | isoclinic class of D33 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C13×D33 |
| unambiguous semidirect product | C3⋊(C3×C7×C13×D11) |
| unambiguous semidirect product | C11⋊(C3×D3×C7×C13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7×C13 | D33 |
| commutator, cosocle, hypocenter | C3×C11 | C2×C3×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C11×C13 | C2 |
| LCS | G ▷ C3×C11 | |
| UCS | C1 ◁ C3×C7×C13 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6006 |
4914 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×D13×D33, C3×D3×C7×C13×D11, C3×C7×D33⋊D13, … |
| maximal normal subgroup of | C3×C7×D13×D33, C3×D3×C7×C13×D11, C3×C7×D33⋊D13, … |
| maximal quotient of | C3×C7×C13×Dic33, C2×C3×C7×C13×D33 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18018, 135);