Finite Group DatabasebetaFinite Group Databasebeta| order | 1092 |
| isoclinism | isoclinic class of D3×D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | D3×C13×D7 |
| unambiguous semidirect product | (D3×C7)⋊(C2×C13) |
| unambiguous semidirect product | (C3×D7)⋊(C2×C13) |
| unambiguous semidirect product | D21⋊(C2×C13) |
| Fitting, socle, Hall | C3×C7×C13 ⋊ C22 |
| derived, Hall | C3×C7 ⋊ C22×C13 |
| Hall | C7×C13 ⋊ C2×D3 |
| Hall | C3×C13 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D3×C13 |
| Sylow | C3 ⋊ C2×C13×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D3×D7 |
| commutator, cosocle, hypocenter | C3×C7 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C13 | C22 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C13 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 273 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | C13×D7×D9, D3×C13×AGL(1,𝔽7), D3×#10587720, … |
| maximal normal subgroup of | D3×C13×AGL(1,𝔽7), D3×#10587720, D3×#10587721, … |
| maximal quotient of | C13×D7×D9, C3×D3×C13×D7, C13×D7×C3⋊D3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1092, 57);