Finite Group DatabasebetaFinite Group Databasebeta| order | 3906 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C3×C31×D21 |
| unambiguous semidirect product | C3⋊(C3×D7×C31) |
| Fitting, socle, Hall | C32×C7×C31 ⋊ C2 |
| derived | C3×C7 ⋊ C2×C3×C31 |
| Hall | C32×C31 ⋊ D7 |
| Hall | C7×C31 ⋊ C3×D3 |
| Hall | C32×C7 ⋊ C2×C31 |
| Sylow | C32 ⋊ D7×C31 |
| Sylow | C7 ⋊ C3×D3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C31 | D21 |
| commutator, cosocle, hypocenter | C3×C7 | C2×C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C31 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C3×C31 | |
36 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 1302 |
1116 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D21×ΓL(1,𝔽32), C3×C31×D105, C3×C5×C31×D21, … |
| maximal normal subgroup of | C3×D21×ΓL(1,𝔽32), C3×C5×C31×D21, C3×C7×C31×D21 |
| maximal quotient of | C3×C31×D105, C3×C5×C31×D21, C3×C31×D147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3906, 67);