Finite Group DatabasebetaFinite Group Databasebeta| order | 10626 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C11⋊(ΓL(1,𝔽8)⋊D23) |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D253 |
| unambiguous semidirect product | C23⋊(C11⋊AGL(1,𝔽7)) |
| unambiguous semidirect product | D1771⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C11×C23 | C2×C3 |
| LCS | G ▷ C7×C11×C23 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,11,23|c^a=c^6,d^a=d^10,e^a=e^22,c^b=c^2637 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10626, 33);