Finite Group DatabasebetaFinite Group Databasebeta| order | 9844 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D23×D107 |
| unambiguous semidirect product | (D23×C107)⋊C2 |
| unambiguous semidirect product | (C23×D107)⋊C2 |
| unambiguous semidirect product | D2461⋊C2 |
| Fitting, socle, derived, Hall | C23×C107 ⋊ C22 |
| Sylow | C107 ⋊ C2×D23 |
| Sylow | C23 ⋊ C2×D107 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C107 | C22 |
| LCS | G ▷ C23×C107 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
715 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D23×D107, D69×D107, D23×D321, … |
| maximal normal subgroup of | C3×D23×D107 |
| maximal quotient of | C3×D23×D107, D69×D107, D23×D321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9844, 6);