Finite Group DatabasebetaFinite Group Databasebeta| order | 8463 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#10620253 |
| Fitting, socle, Hall | C7×C13×C31 ⋊ C3 |
| derived, Hall | C7×C31 ⋊ C3×C13 |
| Hall | C13×C31 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C13 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C13×ΓL(1,𝔽8) |
| Sylow | C7 ⋊ C13×C31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #10620253 |
| commutator, hypocenter | C7×C31 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C31 | C3 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C13 | |
16 conjugacy classes of subgroups.
975 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8463, 7);