Finite Group DatabasebetaFinite Group Databasebeta| order | 6987 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C137⋊C17 |
| unambiguous semidirect product | C137⋊(C3×C17) |
| unambiguous semidirect product | (C3×C137)⋊C17 |
| Fitting, socle, Hall | C3×C137 ⋊ C17 |
| derived, Sylow | C137 ⋊ C3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C137⋊C17 |
| commutator, hypocenter | C137 | C3×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C137 | C17 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C3 | |
8 conjugacy classes of subgroups.
75 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×C137⋊C17, C3×D137⋊C17, D3×C137⋊C17, … |
| maximal normal subgroup of | C2×C3×C137⋊C17, C3×D137⋊C17, D3×C137⋊C17, … |
| maximal quotient of | C2×C3×C137⋊C17, C9×C137⋊C17, C32×C137⋊C17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6987, 1);