Finite Group DatabasebetaFinite Group Databasebeta| order | 8442 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C3 |
| direct product | C7×C3⋊D201 |
| unambiguous semidirect product | C3⋊(C7×D201) |
| unambiguous semidirect product | C67⋊(C7×C3⋊D3) |
| Fitting, socle, Hall | C32×C7×C67 ⋊ C2 |
| derived, Hall | C32×C67 ⋊ C2×C7 |
| Hall | C7×C67 ⋊ C3⋊D3 |
| Sylow | C67 ⋊ C7×C3⋊D3 |
| Hall | C32×C7 ⋊ D67 |
| Sylow | C32 ⋊ C7×D67 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊D201 |
| commutator, hypocenter | C32×C67 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C67 | C2 |
| LCS | G ▷ C32×C67 | |
| UCS | C1 ◁ C7 | |
48 conjugacy classes of subgroups.
2121 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×C3⋊D3×D67, D7×C3⋊D201, D469⋊(C3⋊D3), … |
| maximal normal subgroup of | C7×C3⋊D3×D67, D7×C3⋊D201, D469⋊(C3⋊D3), … |
| maximal quotient of | C7×C3⋊Dic201, C2×C7×C3⋊D201 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8442, 70);