Finite Group DatabasebetaFinite Group Databasebeta| order | 5642 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C13 · Schur multiplier (H2) = C1 |
| direct product | C7×C13×D31 |
| unambiguous semidirect product | C31⋊(C2×C7×C13) |
| Fitting, socle, Hall | C7×C13×C31 ⋊ C2 |
| derived, Sylow | C31 ⋊ C2×C7×C13 |
| Hall | C13×C31 ⋊ C2×C7 |
| Hall | C7×C31 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C13 | D31 |
| commutator, hypocenter | C31 | C2×C7×C13 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C31 | C2 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C7×C13 | |
16 conjugacy classes of subgroups.
1547 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D13×D31, C13×D7×D31, D31×D91, … |
| maximal normal subgroup of | C7×D13×D31, C13×D7×D31, D31×D91, … |
| maximal quotient of | C7×C13×Dic31, C2×C7×C13×D31, C3×C7×C13×D31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5642, 2);