Finite Group DatabasebetaFinite Group Databasebeta| order | 9884 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D353 |
| unambiguous semidirect product | (D7×C353)⋊C2 |
| unambiguous semidirect product | (C7×D353)⋊C2 |
| unambiguous semidirect product | D2471⋊C2 |
| Fitting, socle, derived, Hall | C7×C353 ⋊ C22 |
| Sylow | C353 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D353 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C353 | C22 |
| LCS | G ▷ C7×C353 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
890 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×D353, C3×D7×D353, D21×D353, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D353, C3×D7×D353 |
| maximal quotient of | C3×D7×D353, D21×D353, D7×D1059, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9884, 8);