Finite Group DatabasebetaFinite Group Databasebeta| order | 8092 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D289 |
| unambiguous semidirect product | C289⋊(C22×C7) |
| unambiguous semidirect product | (C2×C289)⋊(C2×C7) |
| Fitting | C2×C7×C289 ⋊ C2 |
| derived, Sylow | C289 ⋊ C22×C7 |
| Hall | C7×C289 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D289 |
| commutator, hypocenter | C289 | C22×C7 |
| Frattini | C17 | C2×C7×D17 |
| Fitting | C2×C7×C289 | C2 |
| socle | C2×C7×C17 | D17 |
| LCS | G ▷ C289 | |
| UCS | C1 ◁ C2×C7 | |
30 conjugacy classes of subgroups.
2044 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×ΓL(1,𝔽8)×D289, D3×C7×D289, C2×C3×C7×D289, … |
| maximal normal subgroup of | C2×ΓL(1,𝔽8)×D289, C2×C3×C7×D289 |
| maximal quotient of | D3×C7×D289, C2×C3×C7×D289, C2×C7×D867 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8092, 9);