Finite Group DatabasebetaFinite Group Databasebeta| order | 6708 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, socle, derived, Hall | C13×C43 ⋊ C22×C3 |
| Hall | D13×D43 ⋊ C3 |
| Hall | C13×C43⋊C3 ⋊ C22 |
| Hall | C43⋊C3 ⋊ C2×D13 |
| Sylow | C43 ⋊ C2×C3×D13 |
| Sylow | C13 ⋊ C2×D43⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C43 | C22×C3 |
| LCS | G ▷ C13×C43 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
104 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×D43⋊C3, C3×D13×D43⋊C3, D39×D43⋊C3, … |
| maximal normal subgroup of | D13⋊C3×D43⋊C3, C3×D13×D43⋊C3, C5×D13×D43⋊C3 |
| maximal quotient of | D13×D43⋊C9, C3×D13×D43⋊C3, D39×D43⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6708, 37);