Finite Group DatabasebetaFinite Group Databasebeta| order | 6825 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C7 · Schur multiplier (H2) = C5 |
| direct product | C7×C13⋊(C52⋊C3) |
| unambiguous semidirect product | C13⋊(C7×C52⋊C3) |
| unambiguous semidirect product | C52⋊(C7×C13⋊C3) |
| Fitting, socle, Hall | C52×C7×C13 ⋊ C3 |
| derived, Hall | C52×C13 ⋊ C3×C7 |
| Hall | C52×C7 ⋊ C13⋊C3 |
| Hall | C7×C13 ⋊ C52⋊C3 |
| Sylow | C52 ⋊ C7×C13⋊C3 |
| Sylow | C13 ⋊ C7×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C13⋊(C52⋊C3) |
| commutator, hypocenter | C52×C13 | C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C13 | C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
777 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6825, 10);