Finite Group DatabasebetaFinite Group Databasebeta| order | 15738 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C43⋊C3)⋊D61 |
| Fitting, socle, derived, Hall | C43×C61 ⋊ C2×C3 |
| Hall | C61×C43⋊C3 ⋊ C2 |
| Hall | D2623 ⋊ C3 |
| Hall | C43⋊C3 ⋊ D61 |
| Sylow | C61 ⋊ D43⋊C3 |
| Sylow | C43 ⋊ C3×D61 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C43×C61 | C2×C3 |
| LCS | G ▷ C43×C61 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2623 |
Polycyclic presentation:
2,3,43,61|c^a=c^42,d^a=d^60,c^b=c^36523 conjugacy classes — view the full character table.
| maximal subgroup of | D61×D43⋊C3, C2×(C43⋊C3)⋊D61 |
| maximal normal subgroup of | D61×D43⋊C3, C2×(C43⋊C3)⋊D61 |
| maximal quotient of | (C43⋊C3)⋊Dic61, C2×(C43⋊C3)⋊D61 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15738, 22);