Finite Group DatabasebetaFinite Group Databasebeta| order | 10716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×C19⋊C3×D47 |
| unambiguous semidirect product | C47⋊(C22×C19⋊C3) |
| unambiguous semidirect product | (C2×C47)⋊(C2×C19⋊C3) |
| unambiguous semidirect product | (C2×C19×D47)⋊C3 |
| Fitting, socle | C2×C19×C47 ⋊ C2×C3 |
| derived, Hall | C19×C47 ⋊ C22×C3 |
| Hall | C2×C19×D47 ⋊ C3 |
| Hall | C47×C19⋊C3 ⋊ C22 |
| Sylow | C47 ⋊ C22×C19⋊C3 |
| Sylow | C19 ⋊ C2×C3×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C19⋊C3×D47 |
| commutator, cosocle, hypocenter | C19×C47 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C47 | C2×C3 |
| LCS | G ▷ C19×C47 | |
| UCS | C1 ◁ C2 | |
40 conjugacy classes of subgroups.
450 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D47×#4296, D3×C19⋊C3×D47, C2×C3×C19⋊C3×D47, … |
| maximal normal subgroup of | C2×D47×#4296, C2×C3×C19⋊C3×D47 |
| maximal quotient of | C2×D47×#4294, D3×C19⋊C3×D47, C2×C3×C19⋊C3×D47, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10716, 17);