Finite Group DatabasebetaFinite Group Databasebeta| order | 7998 |
| isoclinism | isoclinic class of D31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D31⋊C3 |
| unambiguous semidirect product | D31⋊(C3×C43) |
| unambiguous semidirect product | (C31⋊C3)⋊(C2×C43) |
| Fitting, socle, Hall | C31×C43 ⋊ C2×C3 |
| derived, Sylow | C31 ⋊ C2×C3×C43 |
| Hall | C43×C31⋊C3 ⋊ C2 |
| Hall | C43×D31 ⋊ C3 |
| Hall | C31⋊C3 ⋊ C2×C43 |
| Hall | D31 ⋊ C3×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D31⋊C3 |
| commutator, hypocenter | C31 | C2×C3×C43 |
| Frattini | C1 | G |
| Fitting, socle | C31×C43 | C2×C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C43 | |
16 conjugacy classes of subgroups.
473 conjugacy classes — view the full character table.
| maximal subgroup of | D43×D31⋊C3, C2×C43×D31⋊C3, C43⋊C3×D31⋊C3, … |
| maximal normal subgroup of | D43×D31⋊C3, C2×C43×D31⋊C3, C43⋊C3×D31⋊C3, … |
| maximal quotient of | C43×(C31⋊C3)⋊C4, C2×C43×D31⋊C3, C43×D31⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7998, 18);