Finite Group DatabasebetaFinite Group Databasebeta| order | 6612 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D57⋊D29 |
| unambiguous semidirect product | D87⋊D19 |
| unambiguous semidirect product | D551⋊D3 |
| Fitting, socle, derived, Hall | C3×C19×C29 ⋊ C22 |
| Hall | C19×C29 ⋊ C2×D3 |
| Hall | C3×C29 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ C2×D29 |
| Sylow | C29 ⋊ D3×D19 |
| Sylow | C19 ⋊ D3×D29 |
| Sylow | C3 ⋊ D19×D29 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C19×C29 | C22 |
| LCS | G ▷ C3×C19×C29 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,19,29|d^a=d^18,e^a=e^28,c^b=c^2,d^b=d^18453 conjugacy classes — view the full character table.
| maximal subgroup of | D171⋊D29, D87⋊(D19⋊C3), C3×D57⋊D29, … |
| maximal normal subgroup of | D87⋊(D19⋊C3), C3×D57⋊D29, C5×D57⋊D29 |
| maximal quotient of | D171⋊D29, C3×D57⋊D29, D551⋊(C3⋊D3), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6612, 30);