Finite Group DatabasebetaFinite Group Databasebeta| order | 10716 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×Dic47 |
| unambiguous semidirect product | C47⋊(C4×C19⋊C3) |
| unambiguous semidirect product | (C19×Dic47)⋊C3 |
| derived, Hall | C19×C47 ⋊ C3×C4 |
| Hall | C19×Dic47 ⋊ C3 |
| Hall | C47×C19⋊C3 ⋊ C4 |
| Sylow | C47 ⋊ C4×C19⋊C3 |
| Sylow | C19 ⋊ C3×Dic47 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C19⋊C3×D47 |
| commutator, hypocenter | C19×C47 | C3×C4 |
| Fitting, socle, cosocle | C2×C19×C47 | C2×C3 |
| prime radical | C2×C47×C19⋊C3 | C2 |
| LCS | G ▷ C19×C47 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
450 conjugacy classes — view the full character table.
| maximal subgroup of | #4296×Dic47, C3×C19⋊C3×Dic47, C19⋊C3×Dic141 |
| maximal normal subgroup of | #4296×Dic47, C3×C19⋊C3×Dic47 |
| maximal quotient of | #4294×Dic47, C3×C19⋊C3×Dic47, C19⋊C3×Dic141 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10716, 10);