Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×#10587716⋊C2 |
| unambiguous semidirect product | #10587716⋊(C2×C7) |
| unambiguous semidirect product | #10587720⋊(C2×C7) |
| unambiguous semidirect product | #10587722⋊(C2×C7) |
| Fitting, socle, Hall | C72×C13 ⋊ C22×C3 |
| derived | C7×C13 ⋊ C22×C3×C7 |
| Hall | C7×D7×D13 ⋊ C3 |
| Hall | C7×#63270 ⋊ C22 |
| Sylow | C72 ⋊ C2×D13⋊C3 |
| Sylow | C13 ⋊ C2×C7×AGL(1,𝔽7) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #10587716⋊C2 |
| commutator, hypocenter | C7×C13 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C13 | C22×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C7 | |
84 conjugacy classes of subgroups.
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 157);