Finite Group DatabasebetaFinite Group Databasebeta| order | 1596 |
| isoclinism | isoclinic class of D7×D19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D7×D19⋊C3 |
| unambiguous semidirect product | D19⋊(C3×D7) |
| unambiguous semidirect product | (C7×D19⋊C3)⋊C2 |
| unambiguous semidirect product | (D7×C19⋊C3)⋊C2 |
| unambiguous semidirect product | ((C19⋊C3)⋊D7)⋊C2 |
| Fitting, socle, derived, Hall | C7×C19 ⋊ C22×C3 |
| Hall | D7×D19 ⋊ C3 |
| Hall | C7×C19⋊C3 ⋊ C22 |
| Hall | C19⋊C3 ⋊ C2×D7 |
| Sylow | C19 ⋊ C2×C3×D7 |
| Sylow | C7 ⋊ C2×D19⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C19 | C22×C3 |
| LCS | G ▷ C7×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 133 |
45 conjugacy classes — view the full character table.
| maximal subgroup of | #14558801⋊C2, #14558802⋊C2, AGL(1,𝔽7)×D19⋊C3, … |
| maximal normal subgroup of | #14558801⋊C2, #14558802⋊C2, AGL(1,𝔽7)×D19⋊C3, … |
| maximal quotient of | D7×#4294⋊C2, C3×D7×D19⋊C3, D21×D19⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1596, 25);