Finite Group DatabasebetaFinite Group Databasebeta| order | 7998 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C43⋊C3)⋊D31 |
| Fitting, socle, derived, Hall | C31×C43 ⋊ C2×C3 |
| Hall | C31×C43⋊C3 ⋊ C2 |
| Hall | D1333 ⋊ C3 |
| Hall | C43⋊C3 ⋊ D31 |
| Sylow | C43 ⋊ C3×D31 |
| Sylow | C31 ⋊ D43⋊C3 |
| 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.
Polycyclic presentation:
2,3,31,43|c^a=c^30,d^a=d^42,d^b=d^36268 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7998, 21);