Finite Group DatabasebetaFinite Group Databasebeta| order | 8092 |
| isoclinism | isoclinic class of #595 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C7×C17×#595 |
| Fitting, socle, Hall | C7×C172 ⋊ C4 |
| derived | C17 ⋊ C4×C7×C17 |
| Sylow | C172 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C17 | #595 |
| commutator, hypocenter | C17 | C4×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C7×C172 | C4 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C7×C17 | |
32 conjugacy classes of subgroups.
952 conjugacy classes — view the full character table.
| maximal subgroup of | C17×ΓL(1,𝔽8)×#595, C3×C7×C17×#595, C7×C17×C3⋊#595 |
| maximal normal subgroup of | C17×ΓL(1,𝔽8)×#595, C3×C7×C17×#595 |
| maximal quotient of | C3×C7×C17×#595, C7×C17×C3⋊#595 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8092, 19);