Finite Group DatabasebetaFinite Group Databasebeta| order | 7902 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C439 · Schur multiplier (H2) = C3 |
| direct product | C3⋊D3×C439 |
| unambiguous semidirect product | C3⋊(D3×C439) |
| Fitting, socle, Hall | C32×C439 ⋊ C2 |
| derived, Sylow | C32 ⋊ C2×C439 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C439 | C3⋊D3 |
| commutator, hypocenter | C32 | C2×C439 |
| Frattini | C1 | G |
| Fitting, socle | C32×C439 | C2 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C439 | |
24 conjugacy classes of subgroups.
2634 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D3×D439, D32×C439, (C3⋊D3)⋊D439, … |
| maximal normal subgroup of | C3⋊D3×D439, D32×C439, (C3⋊D3)⋊D439, … |
| maximal quotient of | C3⋊Dic3×C439, C2×C3⋊D3×C439 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7902, 15);