Finite Group DatabasebetaFinite Group Databasebeta| order | 8246 |
| isoclinism | isoclinic class of D217 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D217 |
| unambiguous semidirect product | C7⋊(C19×D31) |
| unambiguous semidirect product | C31⋊(D7×C19) |
| Fitting, socle, Hall | C7×C19×C31 ⋊ C2 |
| derived, Hall | C7×C31 ⋊ C2×C19 |
| Hall | C19×C31 ⋊ D7 |
| Hall | C7×C19 ⋊ D31 |
| Sylow | C31 ⋊ D7×C19 |
| Sylow | C7 ⋊ C19×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D217 |
| commutator, hypocenter | C7×C31 | C2×C19 |
| Frattini | C1 | G |
| Fitting, socle | C7×C19×C31 | C2 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C19 | |
16 conjugacy classes of subgroups.
2090 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×C19×D31, D19×D217, D133⋊D31, … |
| maximal normal subgroup of | D7×C19×D31, D19×D217, D133⋊D31, … |
| maximal quotient of | C19×Dic217, C2×C19×D217, C3×C19×D217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8246, 6);