Finite Group DatabasebetaFinite Group Databasebeta| order | 666 |
| isoclinism | isoclinic class of D37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #66524⋊C2 |
| derived, Sylow | C37 ⋊ C2×C9 |
| Hall | #66524 ⋊ C2 |
| Hall | D37 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D37⋊C3 |
| commutator, hypocenter | C37 | C2×C9 |
| Fitting, socle, cosocle | C3×C37 | C2×C3 |
| prime radical | C3×D37 | C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 333 |
Polycyclic presentation:
2,3^2,37|b^3=c,d^a=d^36,d^b=d^2636 conjugacy classes — view the full character table.
| maximal subgroup of | #13050613, C2×#66524⋊C2, #11758603⋊C2, … |
| maximal normal subgroup of | #13050613, C2×#66524⋊C2, #11758603⋊C2, … |
| maximal quotient of | #13050607, C2×#66524⋊C2, #11758601⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(666, 1);