Finite Group DatabasebetaFinite Group Databasebeta| order | 7002 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C3 |
| direct product | C32×D389 |
| unambiguous semidirect product | C389⋊(C2×C32) |
| Fitting, socle, Hall | C32×C389 ⋊ C2 |
| derived, Sylow | C389 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D389 |
| commutator, hypocenter | C389 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C32×C389 | C2 |
| LCS | G ▷ C389 | |
| UCS | C1 ◁ C32 | |
24 conjugacy classes of subgroups.
1764 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×#13095555, C3×C3⋊#13095555, C3×D3×D389, … |
| maximal normal subgroup of | C32×#13095555, C3×C3⋊#13095555, C3×D3×D389, … |
| maximal quotient of | C32×Dic389, C2×C32×D389, C32×C5×D389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7002, 6);