Finite Group DatabasebetaFinite Group Databasebeta| order | 7998 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C31×C43 · Schur multiplier (H2) = C1 |
| direct product | D3×C31×C43 |
| unambiguous semidirect product | C3⋊(C2×C31×C43) |
| Fitting, socle, Hall | C3×C31×C43 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C31×C43 |
| Hall | C3×C43 ⋊ C2×C31 |
| Hall | C3×C31 ⋊ C2×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31×C43 | D3 |
| commutator, hypocenter | C3 | C2×C31×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C31×C43 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C31×C43 | |
16 conjugacy classes of subgroups.
3999 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C31×D43, D3×C43×D31, D3×D1333, … |
| maximal normal subgroup of | D3×C31×D43, D3×C43×D31, D3×D1333, … |
| maximal quotient of | Dic3×C31×C43, C2×D3×C31×C43, D9×C31×C43, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7998, 9);