Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| Fitting, derived, Hall | C13×C49 ⋊ C22×C3 |
| Hall | D13×D49 ⋊ C3 |
| Hall | C13⋊C3×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D13⋊C3 |
| Hall | C13⋊C3 ⋊ C2×D49 |
| Sylow | C13 ⋊ C2×C3×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C49 | C22×C3 |
| Frattini | C7 | D7×D13⋊C3 |
| socle | C7×C13 | C2×C3×D7 |
| LCS | G ▷ C13×C49 | |
| UCS | C1 | |
60 conjugacy classes of subgroups.
208 conjugacy classes — view the full character table.
| maximal subgroup of | D13⋊C3×D49⋊C3, C3×D13⋊C3×D49, D13⋊C3×D147, … |
| maximal normal subgroup of | D13⋊C3×D49⋊C3, C3×D13⋊C3×D49, C5×D13⋊C3×D49 |
| maximal quotient of | D49×D13⋊C9, C3×D13⋊C3×D49, D13⋊C3×D147, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 34);