Finite Group DatabasebetaFinite Group Databasebeta| order | 6734 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13×C37 · Schur multiplier (H2) = C1 |
| direct product | C13×D7×C37 |
| unambiguous semidirect product | C7⋊(C2×C13×C37) |
| Fitting, socle, Hall | C7×C13×C37 ⋊ C2 |
| derived, Sylow | C7 ⋊ C2×C13×C37 |
| Hall | C7×C37 ⋊ C2×C13 |
| Hall | C7×C13 ⋊ C2×C37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C37 | D7 |
| commutator, hypocenter | C7 | C2×C13×C37 |
| Frattini | C1 | G |
| Fitting, socle | C7×C13×C37 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C13×C37 | |
16 conjugacy classes of subgroups.
2405 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×D7×D37, D7×D13×C37, D7×D481, … |
| maximal normal subgroup of | C13×D7×D37, D7×D13×C37, D7×D481, … |
| maximal quotient of | C13×Dic7×C37, C2×C13×D7×C37, C3×C13×D7×C37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6734, 5);