Finite Group DatabasebetaFinite Group Databasebeta| order | 6825 |
| isoclinism | isoclinic class of #63270 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×#63270 |
| Fitting, Hall | C7×C13×C25 ⋊ C3 |
| derived, Hall | C7×C13 ⋊ C3×C25 |
| Hall | C13×C25 ⋊ ΓL(1,𝔽8) |
| Hall | C7×C25 ⋊ C13⋊C3 |
| Sylow | C13 ⋊ ΓL(1,𝔽8)×C25 |
| Sylow | C7 ⋊ C25×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #63270 |
| commutator, hypocenter | C7×C13 | C3×C25 |
| Frattini | C5 | C5×#63270 |
| Fitting | C7×C13×C25 | C3 |
| socle | C5×C7×C13 | C3×C5 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
825 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6825, 5);