Finite Group DatabasebetaFinite Group Databasebeta| order | 9918 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×D87 |
| unambiguous semidirect product | C3⋊(C19⋊C3×D29) |
| unambiguous semidirect product | C29⋊(D3×C19⋊C3) |
| unambiguous semidirect product | (C19×D87)⋊C3 |
| Fitting, socle, derived | C3×C19×C29 ⋊ C2×C3 |
| Hall | C3×C29×C19⋊C3 ⋊ C2 |
| Hall | C19×C29 ⋊ C3×D3 |
| Hall | C3×C19⋊C3 ⋊ D29 |
| Sylow | C29 ⋊ D3×C19⋊C3 |
| Sylow | C19 ⋊ C3×D87 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C29 | C2×C3 |
| LCS | G ▷ C3×C19×C29 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
405 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊C3×D87, D87⋊(D19⋊C3), D3×C19⋊C3×D29, … |
| maximal normal subgroup of | D19⋊C3×D87, D87⋊(D19⋊C3), D3×C19⋊C3×D29, … |
| maximal quotient of | C19⋊C3×Dic87, C2×C19⋊C3×D87 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9918, 24);