Finite Group DatabasebetaFinite Group Databasebeta| order | 7038 |
| isoclinism | isoclinic class of C3⋊D51 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×C3⋊D51 |
| unambiguous semidirect product | C3⋊(C23×D51) |
| unambiguous semidirect product | C17⋊(C3⋊D3×C23) |
| Fitting, socle, Hall | C32×C17×C23 ⋊ C2 |
| derived, Hall | C32×C17 ⋊ C2×C23 |
| Hall | C17×C23 ⋊ C3⋊D3 |
| Hall | C32×C23 ⋊ D17 |
| Sylow | C17 ⋊ C3⋊D3×C23 |
| Sylow | C32 ⋊ C23×D17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊D51 |
| commutator, hypocenter | C32×C17 | C2×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C17×C23 | C2 |
| LCS | G ▷ C32×C17 | |
| UCS | C1 ◁ C23 | |
48 conjugacy classes of subgroups.
1794 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×C3⋊D51, C3⋊D3×C23×D17, D391⋊(C3⋊D3), … |
| maximal normal subgroup of | D23×C3⋊D51, C3⋊D3×C23×D17, D391⋊(C3⋊D3), … |
| maximal quotient of | C23×C3⋊Dic51, C2×C23×C3⋊D51, C5×C23×C3⋊D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7038, 19);