Finite Group DatabasebetaFinite Group Databasebeta| order | 6606 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | D367⋊C9 |
| unambiguous semidirect product | (C367⋊C9)⋊C2 |
| derived, Sylow | C367 ⋊ C2×C9 |
| Hall | C367⋊C9 ⋊ C2 |
| Hall | D367 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D367⋊C3 |
| commutator, hypocenter | C367 | C2×C9 |
| Fitting, socle | C3×C367 | C2×C3 |
| LCS | G ▷ C367 | |
| UCS | C1 ◁ C3 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,367,3|b^3=d,c^a=c^366,c^b=c^283201 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D367⋊C9, C5×D367⋊C9, C5⋊(D367⋊C9) |
| maximal normal subgroup of | C2×D367⋊C9, C5×D367⋊C9 |
| maximal quotient of | Dic367⋊C9, C2×D367⋊C9, C5×D367⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6606, 2);