Finite Group DatabasebetaFinite Group Databasebeta| order | 18786 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D303 |
| unambiguous semidirect product | C3⋊(C31×D101) |
| unambiguous semidirect product | C101⋊(D3×C31) |
| Fitting, socle, Hall | C3×C31×C101 ⋊ C2 |
| derived, Hall | C3×C101 ⋊ C2×C31 |
| Hall | C31×C101 ⋊ D3 |
| Sylow | C101 ⋊ D3×C31 |
| Hall | C3×C31 ⋊ D101 |
| Sylow | C3 ⋊ C31×D101 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D303 |
| commutator, cosocle, hypocenter | C3×C101 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C101 | C2 |
| LCS | G ▷ C3×C101 | |
| UCS | C1 ◁ C31 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9393 |
4743 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C31×D101, D31×D303, D93⋊D101, … |
| maximal normal subgroup of | D3×C31×D101, D31×D303, D93⋊D101, … |
| maximal quotient of | C31×Dic303, C2×C31×D303 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18786, 7);