Finite Group DatabasebetaFinite Group Databasebeta| order | 8036 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D7×D41 |
| unambiguous semidirect product | (D7×C41)⋊(C2×C7) |
| unambiguous semidirect product | (C7×D41)⋊(C2×C7) |
| unambiguous semidirect product | D287⋊(C2×C7) |
| Fitting, socle, Hall | C72×C41 ⋊ C22 |
| derived | C7×C41 ⋊ C22×C7 |
| Sylow | C72 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D7×D41 |
| commutator, hypocenter | C7×C41 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C41 | C22 |
| LCS | G ▷ C7×C41 | |
| UCS | C1 ◁ C7 | |
52 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | D41×#64418, C7×AGL(1,𝔽7)×D41, D7×ΓL(1,𝔽8)×D41, … |
| maximal normal subgroup of | C7×AGL(1,𝔽7)×D41, D7×ΓL(1,𝔽8)×D41, D41×#64423, … |
| maximal quotient of | C3×C7×D7×D41, C7×D21×D41, C7×D7×D123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8036, 21);