Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C2×#16838414 |
| Fitting | C2×C13×C49 ⋊ C2×C3 |
| derived, Hall | C13×C49 ⋊ C22×C3 |
| Hall | C2×D13×C49 ⋊ C3 |
| Hall | #14274255 ⋊ C22 |
| Hall | C2×D13 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ C2×D13⋊C3 |
| Sylow | C13 ⋊ C22×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #16838414 |
| commutator, hypocenter | C13×C49 | C22×C3 |
| Frattini | C7 | C2×#10587717 |
| Fitting | C2×C13×C49 | C2×C3 |
| socle | C2×C7×C13 | C2×ΓL(1,𝔽8) |
| LCS | G ▷ C13×C49 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 43);