Finite Group DatabasebetaFinite Group Databasebeta| order | 6438 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C29⋊(D37⋊C3) |
| unambiguous semidirect product | (C37⋊C3)⋊D29 |
| unambiguous semidirect product | D1073⋊C3 |
| Fitting, socle, derived, Hall | C29×C37 ⋊ C2×C3 |
| Hall | C29×C37⋊C3 ⋊ C2 |
| Hall | D1073 ⋊ C3 |
| Hall | C37⋊C3 ⋊ D29 |
| Sylow | C37 ⋊ C3×D29 |
| Sylow | C29 ⋊ D37⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C29×C37 | C2×C3 |
| LCS | G ▷ C29×C37 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,29,37|c^a=c^28,d^a=d^36,d^b=d^26222 conjugacy classes — view the full character table.
| maximal subgroup of | #16864280⋊C3, #16864281⋊C3, D29×D37⋊C3, … |
| maximal normal subgroup of | #16864280⋊C3, #16864281⋊C3, D29×D37⋊C3, … |
| maximal quotient of | Dic1073⋊C3, C2×C29⋊(D37⋊C3), C29⋊(#66524⋊C2), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6438, 12);