Finite Group DatabasebetaFinite Group Databasebeta| order | 5642 |
| isoclinism | isoclinic class of D91 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D91 |
| unambiguous semidirect product | C7⋊(D13×C31) |
| unambiguous semidirect product | C13⋊(D7×C31) |
| Fitting, socle, Hall | C7×C13×C31 ⋊ C2 |
| derived, Hall | C7×C13 ⋊ C2×C31 |
| Hall | C13×C31 ⋊ D7 |
| Hall | C7×C31 ⋊ D13 |
| Sylow | C13 ⋊ D7×C31 |
| Sylow | C7 ⋊ D13×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D91 |
| commutator, hypocenter | C7×C13 | C2×C31 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C31 | C2 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C31 | |
16 conjugacy classes of subgroups.
1457 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×D91, D7×D13×C31, D91⋊D31, … |
| maximal normal subgroup of | D31×D91, D7×D13×C31, D91⋊D31, … |
| maximal quotient of | C31×Dic91, C2×C31×D91, C3×C31×D91, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5642, 7);