Finite Group DatabasebetaFinite Group Databasebeta| order | 18018 |
| isoclinism | isoclinic class of D231 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C3×C13×D231 |
| unambiguous semidirect product | C3⋊(C3×C13×D77) |
| unambiguous semidirect product | C11⋊(C3×C13×D21) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D231 |
| commutator, cosocle, hypocenter | C3×C7×C11 | C2×C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C11×C13 | C2 |
| LCS | G ▷ C3×C7×C11 | |
| UCS | C1 ◁ C3×C13 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6006 |
4563 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D13×D231, C3×C13×D11×D21, C3×D143⋊D21, … |
| maximal normal subgroup of | C3×D13×D231, C3×C13×D11×D21, C3×D143⋊D21, … |
| maximal quotient of | C3×C13×Dic231, C2×C3×C13×D231 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18018, 131);