Finite Group DatabasebetaFinite Group Databasebeta| order | 8092 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic289 |
| derived, Sylow | C289 ⋊ C4×C7 |
| Hall | C7×C289 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D289 |
| commutator, hypocenter | C289 | C4×C7 |
| Frattini | C2×C17 | C7×D17 |
| Fitting | C2×C7×C289 | C2 |
| socle | C2×C7×C17 | D17 |
| LCS | G ▷ C289 | |
| UCS | C1 ◁ C2×C7 | |
18 conjugacy classes of subgroups.
2044 conjugacy classes. The character table is too large to display.
| maximal subgroup of | ΓL(1,𝔽8)×Dic289, C3×C7×Dic289, C7×Dic867 |
| maximal normal subgroup of | ΓL(1,𝔽8)×Dic289, C3×C7×Dic289 |
| maximal quotient of | C3×C7×Dic289, C7×Dic867 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8092, 3);