Finite Group DatabasebetaFinite Group Databasebeta| order | 7998 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D43×C31⋊C3 |
| Fitting, socle, derived, Hall | C31×C43 ⋊ C2×C3 |
| Hall | C43×C31⋊C3 ⋊ C2 |
| Hall | C31×D43 ⋊ C3 |
| Sylow | C43 ⋊ C2×C31⋊C3 |
| Sylow | C31 ⋊ C3×D43 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C43 | C2×C3 |
| LCS | G ▷ C31×C43 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
299 conjugacy classes — view the full character table.
| maximal subgroup of | D43×D31⋊C3, C2×D43×C31⋊C3, C31⋊C3×D43⋊C3, … |
| maximal normal subgroup of | D43×D31⋊C3, C2×D43×C31⋊C3, C31⋊C3×D43⋊C3, … |
| maximal quotient of | C31⋊C3×Dic43, C2×D43×C31⋊C3, D43×C31⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7998, 14);