Finite Group DatabasebetaFinite Group Databasebeta| order | 10716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C47 · Schur multiplier (H2) = C2 |
| direct product | D3×D19×C47 |
| unambiguous semidirect product | (D3×C19)⋊(C2×C47) |
| unambiguous semidirect product | (C3×D19)⋊(C2×C47) |
| unambiguous semidirect product | D57⋊(C2×C47) |
| Fitting, socle, Hall | C3×C19×C47 ⋊ C22 |
| derived, Hall | C3×C19 ⋊ C22×C47 |
| Hall | C19×C47 ⋊ C2×D3 |
| Hall | C3×C47 ⋊ C2×D19 |
| Sylow | C19 ⋊ C2×D3×C47 |
| Sylow | C3 ⋊ C2×D19×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C47 | D3×D19 |
| commutator, cosocle, hypocenter | C3×C19 | C22×C47 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C47 | C22 |
| LCS | G ▷ C3×C19 | |
| UCS | C1 ◁ C47 | |
40 conjugacy classes of subgroups.
1551 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D9×D19×C47, D3×C47×D19⋊C3, C3×D3×D19×C47, … |
| maximal normal subgroup of | D3×C47×D19⋊C3, C3×D3×D19×C47 |
| maximal quotient of | D9×D19×C47, C3×D3×D19×C47, D3×C47×D57, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10716, 21);