Finite Group DatabasebetaFinite Group Databasebeta| order | 7002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×D389 |
| unambiguous semidirect product | C389⋊(C2×C9) |
| Fitting, Hall | C9×C389 ⋊ C2 |
| derived, Sylow | C389 ⋊ C2×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | D389 |
| commutator, hypocenter | C389 | C2×C9 |
| Frattini | C3 | C3×D389 |
| Fitting | C9×C389 | C2 |
| socle | C3×C389 | C2×C3 |
| LCS | G ▷ C389 | |
| UCS | C1 ◁ C9 | |
12 conjugacy classes of subgroups.
1764 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C9×#13095555, C9⋊#13095555, D9×D389, … |
| maximal normal subgroup of | C9×#13095555, C9⋊#13095555, D9×D389, … |
| maximal quotient of | C9×Dic389, C2×C9×D389, C5×C9×D389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7002, 3);