Finite Group DatabasebetaFinite Group Databasebeta| order | 6690 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C223 · Schur multiplier (H2) = C1 |
| direct product | C5×D3×C223 |
| unambiguous semidirect product | C3⋊(C2×C5×C223) |
| Fitting, socle, Hall | C3×C5×C223 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C5×C223 |
| Hall | C3×C223 ⋊ C2×C5 |
| Hall | C3×C5 ⋊ C2×C223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C223 | D3 |
| commutator, hypocenter | C3 | C2×C5×C223 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C223 | C2 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C5×C223 | |
16 conjugacy classes of subgroups.
3345 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D3×D223, D3×D5×C223, D3×D1115, … |
| maximal normal subgroup of | C5×D3×D223, D3×D5×C223, D3×D1115, … |
| maximal quotient of | C5×Dic3×C223, C2×C5×D3×C223, C5×D9×C223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6690, 6);