Finite Group DatabasebetaFinite Group Databasebeta| order | 10647 |
| automorphism | ? |
| homology | Abelianization (H1) = C7×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C132⋊C7)⋊C9 |
| unambiguous semidirect product | #13095200⋊C7 |
| derived, Sylow | C132 ⋊ C7×C9 |
| Hall | #13095200 ⋊ C7 |
| Hall | C132⋊C7 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #92788⋊C7 |
| commutator, hypocenter | C132 | C7×C9 |
| Fitting, socle, cosocle | C3×C132 | C3×C7 |
| prime radical | C3×C132⋊C7 | C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C3 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
3,7,13^2,3|a^3=e,c^a=c^3,d^a=d^3,c^b=c^3d^11,d^b=c^3d^787 conjugacy classes — view the full character table.
| maximal subgroup of | #14556975⋊C9, ((C13⋊D13)⋊C7)⋊C9, C2×(C132⋊C7)⋊C9 |
| maximal normal subgroup of | #14556975⋊C9, ((C13⋊D13)⋊C7)⋊C9, C2×(C132⋊C7)⋊C9 |
| maximal quotient of | C2×(C132⋊C7)⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10647, 13);