Finite Group DatabasebetaFinite Group Databasebeta| order | 7038 |
| isoclinism | isoclinic class of D207 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×D207 |
| unambiguous semidirect product | C9⋊(C17×D23) |
| unambiguous semidirect product | C23⋊(C17×D9) |
| Fitting, Hall | C9×C17×C23 ⋊ C2 |
| derived, Hall | C9×C23 ⋊ C2×C17 |
| Hall | C17×C23 ⋊ D9 |
| Hall | C9×C17 ⋊ D23 |
| Sylow | C23 ⋊ C17×D9 |
| Sylow | C9 ⋊ C17×D23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | D207 |
| commutator, hypocenter | C9×C23 | C2×C17 |
| Frattini | C3 | C17×D69 |
| Fitting | C9×C17×C23 | C2 |
| socle | C3×C17×C23 | D3 |
| LCS | G ▷ C9×C23 | |
| UCS | C1 ◁ C17 | |
24 conjugacy classes of subgroups.
1785 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C17×D9×D23, D17×D207, D153⋊D23, … |
| maximal normal subgroup of | C17×D9×D23, D17×D207, D153⋊D23, … |
| maximal quotient of | C17×Dic207, C2×C17×D207, C5×C17×D207, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7038, 6);