Finite Group DatabasebetaFinite Group Databasebeta| order | 3906 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×D31⋊C9 |
| unambiguous semidirect product | D31⋊(C7×C9) |
| unambiguous semidirect product | (C31⋊C9)⋊(C2×C7) |
| derived, Sylow | C31 ⋊ C2×C7×C9 |
| Hall | C7×C31⋊C9 ⋊ C2 |
| Hall | C7×D31 ⋊ C9 |
| Hall | C31⋊C9 ⋊ C2×C7 |
| Hall | C7×C31 ⋊ C2×C9 |
| Hall | D31 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D31⋊C3 |
| commutator, hypocenter | C31 | C2×C7×C9 |
| Frattini | C3 | C7×D31⋊C3 |
| Fitting, socle | C3×C7×C31 | C2×C3 |
| prime radical | C3×C7×D31 | C3 |
| cosocle | C3×C31 | C2×C3×C7 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C3×C7 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1953 |
231 conjugacy classes — view the full character table.
| maximal subgroup of | C5×C7×D31⋊C9, C7×C5⋊(D31⋊C9), C7×(D31⋊C5)⋊C9, … |
| maximal normal subgroup of | C5×C7×D31⋊C9, C7×(D31⋊C5)⋊C9, C49×D31⋊C9, … |
| maximal quotient of | C5×C7×D31⋊C9, C7×C5⋊(D31⋊C9), C49×D31⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3906, 2);