Finite Group DatabasebetaFinite Group Databasebeta| order | 8463 |
| isoclinism | isoclinic class of #63271 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#63271 |
| Fitting, socle, Hall | C7×C13×C31 ⋊ C3 |
| derived, Hall | C7×C13 ⋊ C3×C31 |
| Hall | C13×C31 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C31 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×C31 |
| Sylow | C7 ⋊ C31×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #63271 |
| commutator, hypocenter | C7×C13 | C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C31 | C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C31 | |
16 conjugacy classes of subgroups.
1023 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31×#63271, D31×#63271, C31×#10587717, … |
| maximal normal subgroup of | C2×C31×#63271, D31×#63271, C31×#10587717, … |
| maximal quotient of | C2×C31×#63271, C31×#11717942, C3×C31×#63271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8463, 12);