Finite Group DatabasebetaFinite Group Databasebeta| order | 7810 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C71 · Schur multiplier (H2) = C1 |
| direct product | C71×AGL(1,𝔽11) |
| unambiguous semidirect product | D11⋊(C5×C71) |
| unambiguous semidirect product | (C11⋊C5)⋊(C2×C71) |
| Fitting, socle, Hall | C11×C71 ⋊ C2×C5 |
| derived, Sylow | C11 ⋊ C2×C5×C71 |
| Hall | C11⋊C5×C71 ⋊ C2 |
| Hall | D11×C71 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C2×C71 |
| Hall | D11 ⋊ C5×C71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C71 | AGL(1,𝔽11) |
| commutator, hypocenter | C11 | C2×C5×C71 |
| Frattini | C1 | G |
| Fitting, socle | C11×C71 | C2×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C71 | |
16 conjugacy classes of subgroups.
781 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7810, 22);