Finite Group DatabasebetaFinite Group Databasebeta| order | 8484 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C3⋊#87938 |
| unambiguous semidirect product | C3⋊(C7×#87938) |
| Fitting, socle, Hall | C3×C7×C101 ⋊ C4 |
| derived, Hall | C3×C101 ⋊ C4×C7 |
| Hall | C7×C101 ⋊ Dic3 |
| Sylow | C101 ⋊ C7×Dic3 |
| Hall | C3×C7 ⋊ #87938 |
| Sylow | C3 ⋊ C7×#87938 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊#87938 |
| commutator, hypocenter | C3×C101 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C101 | C4 |
| LCS | G ▷ C3×C101 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
567 conjugacy classes — view the full character table.
| maximal subgroup of | C7×C9⋊#87938, ΓL(1,𝔽8)×C3⋊#87938, C3×C7×C3⋊#87938, … |
| maximal normal subgroup of | ΓL(1,𝔽8)×C3⋊#87938, C3×C7×C3⋊#87938 |
| maximal quotient of | C7×C9⋊#87938, C3×C7×C3⋊#87938, C7×C3⋊(C3⋊#87938) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8484, 23);