Finite Group DatabasebetaFinite Group Databasebeta| order | 3210 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D321 |
| unambiguous semidirect product | C3⋊(C5×D107) |
| unambiguous semidirect product | C107⋊(C5×D3) |
| Fitting, socle, Hall | C3×C5×C107 ⋊ C2 |
| derived, Hall | C3×C107 ⋊ C2×C5 |
| Hall | C5×C107 ⋊ D3 |
| Sylow | C107 ⋊ C5×D3 |
| Hall | C3×C5 ⋊ D107 |
| Sylow | C3 ⋊ C5×D107 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D321 |
| commutator, cosocle, hypocenter | C3×C107 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C107 | C2 |
| LCS | G ▷ C3×C107 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 1605 |
810 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×D321, C5×D1605, C52×D321, … |
| maximal normal subgroup of | C25×D321, C52×D321, C5×C7×D321, … |
| maximal quotient of | C25×D321, C5×D1605, C52×D321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3210, 6);