Finite Group DatabasebetaFinite Group Databasebeta| order | 9884 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#13083443 |
| Fitting, socle, Hall | C7×C353 ⋊ C4 |
| derived, Sylow | C353 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #13083443 |
| commutator, hypocenter | C353 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C7×C353 | C4 |
| prime radical | C7×D353 | C2 |
| cosocle | D353 | C2×C7 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C7 | |
12 conjugacy classes of subgroups.
644 conjugacy classes — view the full character table.
| maximal subgroup of | ΓL(1,𝔽8)×#13083443, C3×C7×#13083443, C7×C3⋊#13083443 |
| maximal normal subgroup of | ΓL(1,𝔽8)×#13083443, C3×C7×#13083443 |
| maximal quotient of | C3×C7×#13083443, C7×C3⋊#13083443 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9884, 6);