Finite Group DatabasebetaFinite Group Databasebeta| order | 3390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D565 |
| unambiguous semidirect product | C5⋊(C3×D113) |
| unambiguous semidirect product | C113⋊(C3×D5) |
| Fitting, socle, Hall | C3×C5×C113 ⋊ C2 |
| derived, Hall | C5×C113 ⋊ C2×C3 |
| Hall | C3×C113 ⋊ D5 |
| Sylow | C113 ⋊ C3×D5 |
| Hall | C3×C5 ⋊ D113 |
| Sylow | C5 ⋊ C3×D113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D565 |
| commutator, cosocle, hypocenter | C5×C113 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C113 | C2 |
| LCS | G ▷ C5×C113 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 121 |
| transitive degree | μt(G) = 1695 |
852 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D2825, C3×C5⋊D565, C3×C5×D565, … |
| maximal normal subgroup of | C3×C5×D565, C3×C7×D565, C3×C5⋊(D113⋊C7), … |
| maximal quotient of | C3×D2825, C3×C5⋊D565, C3×C5×D565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3390, 4);