Finite Group DatabasebetaFinite Group Databasebeta| order | 18018 |
| isoclinism | isoclinic class of D143 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C32×C7×D143 |
| unambiguous semidirect product | C11⋊(C32×C7×D13) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C7 | D143 |
| commutator, cosocle, hypocenter | C11×C13 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C11×C13 | C2 |
| LCS | G ▷ C11×C13 | |
| UCS | C1 ◁ C32×C7 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9009 |
4599 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C7×D11×D13, C32×D7×D143, C32×D77⋊D13, … |
| maximal normal subgroup of | C32×C7×D11×D13, C32×D7×D143, C32×D77⋊D13, … |
| maximal quotient of | C32×C7×Dic143, C2×C32×C7×D143 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18018, 142);