Finite Group DatabasebetaFinite Group Databasebeta| order | 9660 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D69⋊D35 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C5×C7×C23 | C22 |
| LCS | G ▷ C3×C5×C7×C23 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,5,7,23|d^a=d^4,e^a=e^6,f^a=f^22,c^b=c^2,d^b=d^4,e^b=e^6651 conjugacy classes — view the full character table.
| maximal subgroup of | D207⋊D35, D69⋊(C5⋊AGL(1,𝔽7)), C3×D69⋊D35, … |
| maximal normal subgroup of | D69⋊(C5⋊AGL(1,𝔽7)), C3×D69⋊D35 |
| maximal quotient of | D207⋊D35, C3×D69⋊D35, D69⋊D105, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9660, 82);