Finite Group DatabasebetaFinite Group Databasebeta| order | 9940 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D35×D71 |
| unambiguous semidirect product | (C5×D71)⋊D7 |
| unambiguous semidirect product | (C7×D71)⋊D5 |
| Fitting, socle, derived, Hall | C5×C7×C71 ⋊ C22 |
| Hall | C7×C71 ⋊ C2×D5 |
| Hall | C5×C71 ⋊ C2×D7 |
| Sylow | C71 ⋊ C2×D35 |
| Hall | C5×C7 ⋊ C2×D71 |
| Sylow | C7 ⋊ D5×D71 |
| Sylow | C5 ⋊ D7×D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C7×C71 | C22 |
| LCS | G ▷ C5×C7×C71 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
703 conjugacy classes — view the full character table.
| maximal subgroup of | D71×C5⋊AGL(1,𝔽7), C3×D35×D71, D71×D105, … |
| maximal normal subgroup of | D71×C5⋊AGL(1,𝔽7), C3×D35×D71 |
| maximal quotient of | C3×D35×D71, D71×D105, D35×D213, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9940, 40);