Finite Group DatabasebetaFinite Group Databasebeta| order | 9918 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | D29×#4294 |
| unambiguous semidirect product | C29⋊(C2×#4294) |
| derived, Hall | C19×C29 ⋊ C2×C9 |
| Hall | C29×#4294 ⋊ C2 |
| Hall | C19×D29 ⋊ C9 |
| Sylow | C29 ⋊ C2×#4294 |
| Sylow | C19 ⋊ C9×D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C19⋊C3×D29 |
| commutator, hypocenter | C19×C29 | C2×C9 |
| Fitting, socle, cosocle | C3×C19×C29 | C2×C3 |
| prime radical | C3×C19×D29 | C3 |
| LCS | G ▷ C19×C29 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
432 conjugacy classes — view the full character table.
| maximal subgroup of | #4294⋊#1181, D29×#4294⋊C2, #1181×#4294, … |
| maximal normal subgroup of | #4294⋊#1181, D29×#4294⋊C2, #1181×#4294, … |
| maximal quotient of | Dic29×#4294, C2×D29×#4294 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9918, 10);