Finite Group DatabasebetaFinite Group Databasebeta| order | 10626 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C7⋊AGL(1,𝔽23)) |
| unambiguous semidirect product | C7⋊(C3⋊AGL(1,𝔽23)) |
| unambiguous semidirect product | (C23⋊C11)⋊D21 |
| unambiguous semidirect product | D483⋊C11 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C7×C23 | C2×C11 |
| LCS | G ▷ C3×C7×C23 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,11,23|b^a=b^2,c^a=c^6,e^a=e^22,e^d=e^2153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10626, 26);