Finite Group DatabasebetaFinite Group Databasebeta| order | 15762 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C71⋊(D37⋊C3) |
| unambiguous semidirect product | (C37⋊C3)⋊D71 |
| unambiguous semidirect product | D2627⋊C3 |
| Fitting, socle, derived, Hall | C37×C71 ⋊ C2×C3 |
| Hall | C71×C37⋊C3 ⋊ C2 |
| Hall | D2627 ⋊ C3 |
| Hall | C37⋊C3 ⋊ D71 |
| Sylow | C71 ⋊ D37⋊C3 |
| Sylow | C37 ⋊ C3×D71 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C37×C71 | C2×C3 |
| LCS | G ▷ C37×C71 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2627 |
Polycyclic presentation:
2,3,37,71|c^a=c^36,d^a=d^70,c^b=c^26537 conjugacy classes — view the full character table.
| maximal subgroup of | D71×D37⋊C3, C2×C71⋊(D37⋊C3) |
| maximal normal subgroup of | D71×D37⋊C3, C2×C71⋊(D37⋊C3) |
| maximal quotient of | C71⋊(Dic37⋊C3), C2×C71⋊(D37⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15762, 12);