Finite Group DatabasebetaFinite Group Databasebeta| order | 6882 |
| isoclinism | isoclinic class of D37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×D37⋊C3 |
| unambiguous semidirect product | D37⋊(C3×C31) |
| unambiguous semidirect product | (C37⋊C3)⋊(C2×C31) |
| Fitting, socle, Hall | C31×C37 ⋊ C2×C3 |
| derived, Sylow | C37 ⋊ C2×C3×C31 |
| Hall | C31×C37⋊C3 ⋊ C2 |
| Hall | C31×D37 ⋊ C3 |
| Hall | C37⋊C3 ⋊ C2×C31 |
| Hall | D37 ⋊ C3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | D37⋊C3 |
| commutator, hypocenter | C37 | C2×C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C37 | C2×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C31 | |
16 conjugacy classes of subgroups.
372 conjugacy classes — view the full character table.
| maximal subgroup of | C31×#3866⋊C3, #28351811, D31×D37⋊C3, … |
| maximal normal subgroup of | C31×#3866⋊C3, #28351811, D31×D37⋊C3, … |
| maximal quotient of | C31×Dic37⋊C3, C2×C31×D37⋊C3, C31×#66524⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6882, 13);