Finite Group DatabasebetaFinite Group Databasebeta| order | 741 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×C19⋊C3 |
| unambiguous semidirect product | C19⋊(C3×C13) |
| Fitting, socle, Hall | C13×C19 ⋊ C3 |
| derived, Sylow | C19 ⋊ C3×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C19 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 247 |
117 conjugacy classes — view the full character table.
| maximal subgroup of | C13×D19⋊C3, D13×C19⋊C3, (C19⋊C3)⋊D13, … |
| maximal normal subgroup of | C13×D19⋊C3, D13×C19⋊C3, (C19⋊C3)⋊D13, … |
| maximal quotient of | C2×C13×C19⋊C3, C13×#4294, C3×C13×C19⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(741, 2);