Finite Group DatabasebetaFinite Group Databasebeta| order | 10716 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D57⋊D47 |
| unambiguous semidirect product | D141⋊D19 |
| unambiguous semidirect product | D893⋊D3 |
| Fitting, socle, derived, Hall | C3×C19×C47 ⋊ C22 |
| Hall | C19×C47 ⋊ C2×D3 |
| Hall | C3×C47 ⋊ C2×D19 |
| Hall | C3×C19 ⋊ C2×D47 |
| Sylow | C47 ⋊ D3×D19 |
| Sylow | C19 ⋊ D3×D47 |
| Sylow | C3 ⋊ D19×D47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C47 | C22 |
| LCS | G ▷ C3×C19×C47 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3,19,47|d^a=d^18,e^a=e^46,c^b=c^2,d^b=d^18723 conjugacy classes — view the full character table.
| maximal subgroup of | D171⋊D47, D141⋊(D19⋊C3), C3×D57⋊D47, … |
| maximal normal subgroup of | D141⋊(D19⋊C3), C3×D57⋊D47 |
| maximal quotient of | D171⋊D47, C3×D57⋊D47, D141⋊D57, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10716, 24);