Finite Group DatabasebetaFinite Group Databasebeta| order | 8442 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1407 |
| unambiguous semidirect product | C7⋊(C3⋊D201) |
| unambiguous semidirect product | C67⋊(C3⋊D21) |
| Fitting, socle, derived, Hall | C32×C7×C67 ⋊ C2 |
| Hall | C32×C67 ⋊ D7 |
| Hall | C7×C67 ⋊ C3⋊D3 |
| Sylow | C67 ⋊ C3⋊D21 |
| Hall | C32×C7 ⋊ D67 |
| Sylow | C32 ⋊ D469 |
| Sylow | C7 ⋊ C3⋊D201 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C7×C67 | C2 |
| LCS | G ▷ C32×C7×C67 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,7,67|b^a=b^2,c^a=c^2,d^a=d^6,e^a=e^662112 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3⋊D21×D67, D7×C3⋊D201, C3⋊D3×D469, … |
| maximal normal subgroup of | C3⋊D21×D67, D7×C3⋊D201, C3⋊D3×D469, … |
| maximal quotient of | C3⋊Dic1407, C2×C3⋊D1407 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8442, 72);