Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C3⋊(C7⋊#261) |
| unambiguous semidirect product | C3⋊(C7×C7⋊#261) |
| unambiguous semidirect product | C7⋊(C7×C3⋊#261) |
| Fitting, socle, Hall | C3×C72×C13 ⋊ C4 |
| derived | C3×C7×C13 ⋊ C4×C7 |
| Hall | C72×C13 ⋊ Dic3 |
| Hall | C3×C72 ⋊ #261 |
| Sylow | C72 ⋊ C3⋊#261 |
| Hall | C3×C13 ⋊ C7×Dic7 |
| Sylow | C13 ⋊ C7×Dic21 |
| Sylow | C3 ⋊ C7×C7⋊#261 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊(C7⋊#261) |
| commutator, hypocenter | C3×C7×C13 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C13 | C4 |
| LCS | G ▷ C3×C7×C13 | |
| UCS | C1 ◁ C7 | |
72 conjugacy classes of subgroups.
609 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 326);