Finite Group DatabasebetaFinite Group Databasebeta| order | 6441 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C113 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×C113 |
| unambiguous semidirect product | C19⋊(C3×C113) |
| unambiguous semidirect product | (C19×C113)⋊C3 |
| Fitting, socle, Hall | C19×C113 ⋊ C3 |
| derived, Sylow | C19 ⋊ C3×C113 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C113 | C19⋊C3 |
| commutator, hypocenter | C19 | C3×C113 |
| Frattini | C1 | G |
| Fitting, socle | C19×C113 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C113 | |
8 conjugacy classes of subgroups.
1017 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C19⋊C3×C113, C19⋊C3×D113, C113×D19⋊C3, … |
| maximal normal subgroup of | C2×C19⋊C3×C113, C19⋊C3×D113, C113×D19⋊C3, … |
| maximal quotient of | C2×C19⋊C3×C113, C113×#4294, C3×C19⋊C3×C113, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6441, 1);