Finite Group DatabasebetaFinite Group Databasebeta| order | 3906 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D279 |
| unambiguous semidirect product | C9⋊(C7×D31) |
| unambiguous semidirect product | C31⋊(C7×D9) |
| Fitting, Hall | C7×C9×C31 ⋊ C2 |
| derived, Hall | C9×C31 ⋊ C2×C7 |
| Hall | C7×C31 ⋊ D9 |
| Hall | C7×C9 ⋊ D31 |
| Sylow | C31 ⋊ C7×D9 |
| Sylow | C9 ⋊ C7×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D279 |
| commutator, cosocle, hypocenter | C9×C31 | C2×C7 |
| Frattini | C3 | C7×D93 |
| Fitting | C7×C9×C31 | C2 |
| socle | C3×C7×C31 | D3 |
| LCS | G ▷ C9×C31 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1953 |
987 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×C7×D279, C7×D1395, C7×C9⋊(D31⋊C5), … |
| maximal normal subgroup of | C5×C7×D279, C7×C9⋊(D31⋊C5), C49×D279, … |
| maximal quotient of | C5×C7×D279, C7×D1395, C49×D279, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3906, 22);