Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | #261×C49⋊C3 |
| Fitting, derived, Hall | C13×C49 ⋊ C3×C4 |
| Hall | C49×#261 ⋊ C3 |
| Hall | C13×C49⋊C3 ⋊ C4 |
| Sylow | C49 ⋊ C3×#261 |
| Sylow | C13 ⋊ C4×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C13×C49 | C3×C4 |
| Frattini | C7 | ΓL(1,𝔽8)×#261 |
| socle | C7×C13 | C4×ΓL(1,𝔽8) |
| LCS | G ▷ C13×C49 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
133 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 28);