Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D13×D147 |
| unambiguous semidirect product | (C3×D13)⋊D49 |
| unambiguous semidirect product | (D13×C49)⋊D3 |
| Fitting, derived, Hall | C3×C13×C49 ⋊ C22 |
| Hall | C13×C49 ⋊ C2×D3 |
| Hall | C3×C49 ⋊ C2×D13 |
| Sylow | C49 ⋊ D3×D13 |
| Hall | C3×C13 ⋊ C2×D49 |
| Sylow | C13 ⋊ C2×D147 |
| Sylow | C3 ⋊ D13×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C3×C13×C49 | C22 |
| Frattini | C7 | D13×D21 |
| socle | C3×C7×C13 | C2×D7 |
| LCS | G ▷ C3×C13×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
600 conjugacy classes — view the full character table.
| maximal subgroup of | D13×D441, #16838413⋊D3, #16838414⋊D3, … |
| maximal normal subgroup of | #16838413⋊D3, #16838414⋊D3, D13×C3⋊(D49⋊C3), … |
| maximal quotient of | D13×D441, C3×D13×D147, D13×C3⋊D147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 56);