Finite Group DatabasebetaFinite Group Databasebeta| order | 9918 |
| isoclinism | isoclinic class of D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#4294⋊C2 |
| unambiguous semidirect product | #4294⋊(C2×C29) |
| derived, Sylow | C19 ⋊ C2×C9×C29 |
| Hall | C29×#4294 ⋊ C2 |
| Hall | C29×D19 ⋊ C9 |
| Hall | C19×C29 ⋊ C2×C9 |
| Hall | #4294 ⋊ C2×C29 |
| Hall | D19 ⋊ C9×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C29 | D19⋊C3 |
| commutator, hypocenter | C19 | C2×C9×C29 |
| Frattini | C3 | C29×D19⋊C3 |
| Fitting, socle | C3×C19×C29 | C2×C3 |
| prime radical | C3×C29×D19 | C3 |
| cosocle | C3×C19 | C2×C3×C29 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C3×C29 | |
24 conjugacy classes of subgroups.
783 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#4294⋊C2, C2×C29×#4294⋊C2 |
| maximal normal subgroup of | D29×#4294⋊C2, C2×C29×#4294⋊C2 |
| maximal quotient of | C29×#4294⋊C4, C2×C29×#4294⋊C2 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9918, 11);