Finite Group DatabasebetaFinite Group Databasebeta| order | 1206 |
| isoclinism | isoclinic class of D67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D67⋊C9 |
| unambiguous semidirect product | (C67⋊C9)⋊C2 |
| derived, Sylow | C67 ⋊ C2×C9 |
| Hall | C67⋊C9 ⋊ C2 |
| Hall | D67 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D67⋊C3 |
| commutator, hypocenter | C67 | C2×C9 |
| Fitting, socle, cosocle | C3×C67 | C2×C3 |
| prime radical | C3×D67 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 76 |
| transitive degree | μt(G) = 603 |
Polycyclic presentation:
2,3^2,67|b^3=c,d^a=d^66,d^b=d^3751 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D67⋊C9, C11×D67⋊C9, C11⋊(D67⋊C9), … |
| maximal normal subgroup of | C2×D67⋊C9, C11×D67⋊C9, (D67⋊C9)⋊C11, … |
| maximal quotient of | Dic67⋊C9, C2×D67⋊C9, C11×D67⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1206, 1);