Finite Group DatabasebetaFinite Group Databasebeta| order | 9738 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C2×#19096459 |
| Fitting, socle, Hall | C2×C541 ⋊ C9 |
| derived, Sylow | C541 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19096459 |
| commutator, hypocenter | C541 | C2×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C541 | C9 |
| prime radical | C2×C541⋊C3 | C3 |
| cosocle | C541⋊C3 | C2×C3 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
138 conjugacy classes — view the full character table.
| maximal subgroup of | #34085791, C4×#19096459, C2×#19096459⋊C2, … |
| maximal normal subgroup of | #34085791, C4×#19096459, C2×#19096459⋊C2, … |
| maximal quotient of | C4×#19096459, C22×#19096459 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9738, 9);