Finite Group DatabasebetaFinite Group Databasebeta| order | 8085 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C7 |
| direct product | C11⋊C5×#3862 |
| unambiguous semidirect product | C11⋊(C5×#3862) |
| unambiguous semidirect product | (C11×#3862)⋊C5 |
| Fitting, socle, derived, Hall | C72×C11 ⋊ C3×C5 |
| Hall | C72×C11⋊C5 ⋊ C3 |
| Hall | C11×#3862 ⋊ C5 |
| Sylow | C72 ⋊ C3×C11⋊C5 |
| Sylow | C11 ⋊ C5×#3862 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C11 | C3×C5 |
| LCS | G ▷ C72×C11 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
133 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8085, 8);