Finite Group DatabasebetaFinite Group Databasebeta| order | 3870 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1 |
| direct product | C5×D43⋊C9 |
| unambiguous semidirect product | D43⋊(C5×C9) |
| unambiguous semidirect product | (C43⋊C9)⋊(C2×C5) |
| unambiguous semidirect product | (C5×D43)⋊C9 |
| derived, Sylow | C43 ⋊ C2×C5×C9 |
| Hall | C5×C43⋊C9 ⋊ C2 |
| Hall | C5×D43 ⋊ C9 |
| Hall | C43⋊C9 ⋊ C2×C5 |
| Hall | C5×C43 ⋊ C2×C9 |
| Hall | D43 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5 | D43⋊C3 |
| commutator, hypocenter | C43 | C2×C5×C9 |
| Frattini | C3 | C5×D43⋊C3 |
| Fitting, socle | C3×C5×C43 | C2×C3 |
| prime radical | C3×C5×D43 | C3 |
| cosocle | C3×C43 | C2×C3×C5 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3×C5 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1935 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | C25×D43⋊C9, C52×D43⋊C9, C5×C5⋊(D43⋊C9), … |
| maximal normal subgroup of | C25×D43⋊C9, C52×D43⋊C9, C5×C7×D43⋊C9, … |
| maximal quotient of | C25×D43⋊C9, C52×D43⋊C9, C5×C5⋊(D43⋊C9), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3870, 2);