Finite Group DatabasebetaFinite Group Databasebeta| order | 8742 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C31⋊C3×D47 |
| unambiguous semidirect product | C47⋊(C2×C31⋊C3) |
| unambiguous semidirect product | (C31×D47)⋊C3 |
| Fitting, socle, derived, Hall | C31×C47 ⋊ C2×C3 |
| Hall | C47×C31⋊C3 ⋊ C2 |
| Hall | C31×D47 ⋊ C3 |
| Sylow | C47 ⋊ C2×C31⋊C3 |
| Sylow | C31 ⋊ C3×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C31×C47 | C2×C3 |
| LCS | G ▷ C31×C47 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
325 conjugacy classes — view the full character table.
| maximal subgroup of | D47×D31⋊C3, C2×C31⋊C3×D47, C3×C31⋊C3×D47, … |
| maximal normal subgroup of | D47×D31⋊C3, C2×C31⋊C3×D47, C3×C31⋊C3×D47 |
| maximal quotient of | C31⋊C3×Dic47, C2×C31⋊C3×D47, D47×C31⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8742, 10);