Finite Group DatabasebetaFinite Group Databasebeta| order | 15762 |
| isoclinism | isoclinic class of D213 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×D213 |
| unambiguous semidirect product | C3⋊(C37×D71) |
| unambiguous semidirect product | C71⋊(D3×C37) |
| Fitting, socle, Hall | C3×C37×C71 ⋊ C2 |
| derived, Hall | C3×C71 ⋊ C2×C37 |
| Hall | C37×C71 ⋊ D3 |
| Hall | C3×C37 ⋊ D71 |
| Sylow | C71 ⋊ D3×C37 |
| Sylow | C3 ⋊ C37×D71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C37 | D213 |
| commutator, cosocle, hypocenter | C3×C71 | C2×C37 |
| Frattini | C1 | G |
| Fitting, socle | C3×C37×C71 | C2 |
| LCS | G ▷ C3×C71 | |
| UCS | C1 ◁ C37 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7881 |
3996 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C37×D71, D37×D213, D111⋊D71, … |
| maximal normal subgroup of | D3×C37×D71, D37×D213, D111⋊D71, … |
| maximal quotient of | C37×Dic213, C2×C37×D213 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15762, 7);