Finite Group DatabasebetaFinite Group Databasebeta| order | 7011 |
| isoclinism | isoclinic class of #4296 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×#4296 |
| Fitting, socle, Hall | C19×C41 ⋊ C9 |
| derived, Sylow | C19 ⋊ C9×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | #4296 |
| commutator, hypocenter | C19 | C9×C41 |
| Frattini | C1 | G |
| Fitting, socle | C19×C41 | C9 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C41 | |
12 conjugacy classes of subgroups.
451 conjugacy classes — view the full character table.
| maximal subgroup of | C41×AGL(1,𝔽19), C41⋊AGL(1,𝔽19), D41×#4296, … |
| maximal normal subgroup of | C41×AGL(1,𝔽19), C41⋊AGL(1,𝔽19), D41×#4296, … |
| maximal quotient of | C2×C41×#4296, C41×C22⋊#4296, C5×C41×#4296 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7011, 4);