Finite Group DatabasebetaFinite Group Databasebeta| order | 8036 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C7⋊#4223 |
| unambiguous semidirect product | C7⋊(C7×#4223) |
| Fitting, socle, Hall | C72×C41 ⋊ C4 |
| derived | C7×C41 ⋊ C4×C7 |
| Sylow | C72 ⋊ #4223 |
| Sylow | C41 ⋊ C7×Dic7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C7⋊#4223 |
| commutator, hypocenter | C7×C41 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C41 | C4 |
| LCS | G ▷ C7×C41 | |
| UCS | C1 ◁ C7 | |
36 conjugacy classes of subgroups.
560 conjugacy classes — view the full character table.
| maximal subgroup of | #37563072, C7×ΓL(1,𝔽8)⋊#4223, ΓL(1,𝔽8)×C7⋊#4223, … |
| maximal normal subgroup of | C7×ΓL(1,𝔽8)⋊#4223, ΓL(1,𝔽8)×C7⋊#4223, #37563094, … |
| maximal quotient of | C3×C7×C7⋊#4223, C7×C3⋊(C7⋊#4223) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8036, 20);