Finite Group DatabasebetaFinite Group Databasebeta| order | 9884 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D353 |
| unambiguous semidirect product | C353⋊(C22×C7) |
| unambiguous semidirect product | (C2×C353)⋊(C2×C7) |
| Fitting, socle | C2×C7×C353 ⋊ C2 |
| derived, Sylow | C353 ⋊ C22×C7 |
| Hall | C7×C353 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D353 |
| commutator, cosocle, hypocenter | C353 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C353 | C2 |
| LCS | G ▷ C353 | |
| UCS | C1 ◁ C2×C7 | |
20 conjugacy classes of subgroups.
2492 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×ΓL(1,𝔽8)×D353, D3×C7×D353, C2×C3×C7×D353, … |
| maximal normal subgroup of | C2×ΓL(1,𝔽8)×D353, C2×C3×C7×D353 |
| maximal quotient of | D3×C7×D353, C2×C3×C7×D353, C2×C7×D1059 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9884, 11);