Finite Group DatabasebetaFinite Group Databasebeta| order | 3342 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D557 |
| unambiguous semidirect product | C557⋊(C2×C3) |
| Fitting, socle, Hall | C3×C557 ⋊ C2 |
| derived, Sylow | C557 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D557 |
| commutator, cosocle, hypocenter | C557 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C557 | C2 |
| LCS | G ▷ C557 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 560 |
| transitive degree | μt(G) = 1671 |
840 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D557, C3×D2785, C3×C7×D557, … |
| maximal normal subgroup of | C3×C5×D557, C3×C7×D557, C3×C11×D557 |
| maximal quotient of | C3×C5×D557, C3×D2785, C3×C7×D557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3342, 2);