Finite Group DatabasebetaFinite Group Databasebeta| order | 6690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1115 |
| unambiguous semidirect product | C5⋊(C3×D223) |
| Fitting, socle, Hall | C3×C5×C223 ⋊ C2 |
| derived, Hall | C5×C223 ⋊ C2×C3 |
| Hall | C3×C223 ⋊ D5 |
| Sylow | C223 ⋊ C3×D5 |
| Hall | C3×C5 ⋊ D223 |
| Sylow | C5 ⋊ C3×D223 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1115 |
| commutator, hypocenter | C5×C223 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C223 | C2 |
| LCS | G ▷ C5×C223 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
1677 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×D223, D3×D1115, D15⋊D223, … |
| maximal normal subgroup of | C3×D5×D223, D3×D1115, D15⋊D223, … |
| maximal quotient of | C3×Dic1115, C2×C3×D1115, C9×D1115, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6690, 5);