Finite Group DatabasebetaFinite Group Databasebeta| order | 9366 |
| isoclinism | isoclinic class of D223 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×D223 |
| Fitting, socle, Hall | C3×C7×C223 ⋊ C2 |
| derived, Sylow | C223 ⋊ C2×C3×C7 |
| Hall | C7×C223 ⋊ C2×C3 |
| Hall | C3×C223 ⋊ C2×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D223 |
| commutator, hypocenter | C223 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C223 | C2 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C3×C7 | |
16 conjugacy classes of subgroups.
2373 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D7×D223, D3×C7×D223, D21×D223, … |
| maximal normal subgroup of | C3×D7×D223, D3×C7×D223, D21×D223, … |
| maximal quotient of | C3×C7×Dic223, C2×C3×C7×D223, C7×C9×D223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9366, 6);