Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×(C13⋊C3)⋊D7 |
| unambiguous semidirect product | (C2×C13⋊C3)⋊(C7×D7) |
| Fitting, socle | C2×C72×C13 ⋊ C2×C3 |
| derived | C7×C13 ⋊ C22×C3×C7 |
| Hall | C2×C7×D91 ⋊ C3 |
| Hall | C72×C13⋊C3 ⋊ C22 |
| Hall | C72×C13 ⋊ C22×C3 |
| Sylow | C72 ⋊ C2×D13⋊C3 |
| Hall | C13⋊C3 ⋊ C2×C7×D7 |
| Sylow | C13 ⋊ C2×C3×C7×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | (C13⋊C3)⋊D7 |
| commutator, hypocenter | C7×C13 | C22×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C13 | C2×C3 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C2×C7 | |
104 conjugacy classes of subgroups.
406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 268);