Finite Group DatabasebetaFinite Group Databasebeta| order | 7138 |
| isoclinism | isoclinic class of D83 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D83 |
| unambiguous semidirect product | C83⋊(C2×C43) |
| Fitting, socle, Hall | C43×C83 ⋊ C2 |
| derived, Sylow | C83 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D83 |
| commutator, hypocenter | C83 | C2×C43 |
| Frattini | C1 | G |
| Fitting, socle | C43×C83 | C2 |
| LCS | G ▷ C83 | |
| UCS | C1 ◁ C43 | |
8 conjugacy classes of subgroups.
1849 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D83, C2×C43×D83, C3×C43×D83, … |
| maximal normal subgroup of | D43×D83, C2×C43×D83, C3×C43×D83, … |
| maximal quotient of | C43×Dic83, C2×C43×D83, C3×C43×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7138, 2);