Finite Group DatabasebetaFinite Group Databasebeta| order | 7626 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C41⋊(D31⋊C3) |
| unambiguous semidirect product | (C31⋊C3)⋊D41 |
| unambiguous semidirect product | D1271⋊C3 |
| Fitting, socle, derived, Hall | C31×C41 ⋊ C2×C3 |
| Hall | C41×C31⋊C3 ⋊ C2 |
| Hall | D1271 ⋊ C3 |
| Hall | C31⋊C3 ⋊ D41 |
| Sylow | C41 ⋊ D31⋊C3 |
| Sylow | C31 ⋊ C3×D41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C41 | C2×C3 |
| LCS | G ▷ C31×C41 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,31,41|c^a=c^30,d^a=d^40,c^b=c^25271 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7626, 12);