Finite Group DatabasebetaFinite Group Databasebeta| order | 6708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C13 · Schur multiplier (H2) = C2 |
| direct product | D3×C13×D43 |
| unambiguous semidirect product | (D3×C43)⋊(C2×C13) |
| unambiguous semidirect product | (C3×D43)⋊(C2×C13) |
| unambiguous semidirect product | D129⋊(C2×C13) |
| Fitting, socle, Hall | C3×C13×C43 ⋊ C22 |
| derived, Hall | C3×C43 ⋊ C22×C13 |
| Hall | C13×C43 ⋊ C2×D3 |
| Sylow | C43 ⋊ C2×D3×C13 |
| Hall | C3×C13 ⋊ C2×D43 |
| Sylow | C3 ⋊ C2×C13×D43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D3×D43 |
| commutator, hypocenter | C3×C43 | C22×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C43 | C22 |
| LCS | G ▷ C3×C43 | |
| UCS | C1 ◁ C13 | |
40 conjugacy classes of subgroups.
897 conjugacy classes — view the full character table.
| maximal subgroup of | C13×D9×D43, D3×C13×D43⋊C3, D3×#16809809, … |
| maximal normal subgroup of | D3×C13×D43⋊C3, D3×#16809809, D3×#16809810, … |
| maximal quotient of | C13×D9×D43, C3×D3×C13×D43, D3×C13×D129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6708, 53);