Finite Group DatabasebetaFinite Group Databasebeta| order | 612 |
| isoclinism | isoclinic class of D3×D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D3×D17 |
| unambiguous semidirect product | (D3×C17)⋊(C2×C3) |
| unambiguous semidirect product | (C3×D17)⋊(C2×C3) |
| unambiguous semidirect product | D51⋊(C2×C3) |
| Fitting, socle, Hall | C32×C17 ⋊ C22 |
| derived | C3×C17 ⋊ C22×C3 |
| Sylow | C17 ⋊ C2×C3×D3 |
| Sylow | C32 ⋊ C2×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×D17 |
| commutator, cosocle, hypocenter | C3×C17 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17 | C22 |
| LCS | G ▷ C3×C17 | |
| UCS | C1 ◁ C3 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 102 |
90 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D3×#595, D3×C3⋊#595, D32×D17, … |
| maximal normal subgroup of | C3×D3×#595, D3×C3⋊#595, D32×D17, … |
| maximal quotient of | C3×Dic3×D17, C3×D3×Dic17, C3×#87972, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(612, 25);