Finite Group DatabasebetaFinite Group Databasebeta| order | 8036 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D287 |
| unambiguous semidirect product | (C7×D7)⋊D41 |
| unambiguous semidirect product | (D7×C41)⋊D7 |
| Fitting, socle, derived, Hall | C72×C41 ⋊ C22 |
| Sylow | C72 ⋊ C2×D41 |
| Sylow | C41 ⋊ D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C41 | C22 |
| LCS | G ▷ C72×C41 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
725 conjugacy classes — view the full character table.
| maximal subgroup of | #64418⋊D41, D7×ΓL(1,𝔽8)⋊D41, AGL(1,𝔽7)×D287, … |
| maximal normal subgroup of | D7×ΓL(1,𝔽8)⋊D41, AGL(1,𝔽7)×D287, #64423⋊D41, … |
| maximal quotient of | C3×D7×D287, D7×D861, D21×D287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8036, 25);