Finite Group DatabasebetaFinite Group Databasebeta| order | 15762 |
| isoclinism | isoclinic class of D37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×D37⋊C3 |
| unambiguous semidirect product | D37⋊(C3×C71) |
| unambiguous semidirect product | (C37⋊C3)⋊(C2×C71) |
| unambiguous semidirect product | (C71×D37)⋊C3 |
| Fitting, socle, Hall | C37×C71 ⋊ C2×C3 |
| derived, Sylow | C37 ⋊ C2×C3×C71 |
| Hall | C71×C37⋊C3 ⋊ C2 |
| Hall | C71×D37 ⋊ C3 |
| Hall | C37⋊C3 ⋊ C2×C71 |
| Hall | D37 ⋊ C3×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | D37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C2×C3×C71 |
| Frattini | C1 | G |
| Fitting, socle | C37×C71 | C2×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C71 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2627 |
852 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C71×#3866⋊C3, C71⋊(#3866⋊C3), D71×D37⋊C3, … |
| maximal normal subgroup of | C71×#3866⋊C3, C71⋊(#3866⋊C3), D71×D37⋊C3, … |
| maximal quotient of | C71×Dic37⋊C3, C2×C71×D37⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15762, 11);