Finite Group DatabasebetaFinite Group Databasebeta| order | 7644 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#11763981 |
| Fitting, socle, Hall | C72×C13 ⋊ C3×C4 |
| derived | C7×C13 ⋊ C3×C4×C7 |
| Hall | C72×#261 ⋊ C3 |
| Hall | C7×#63271 ⋊ C4 |
| Hall | #261 ⋊ C7×ΓL(1,𝔽8) |
| Sylow | C72 ⋊ AGL(1,𝔽13) |
| Sylow | C13 ⋊ C4×C7×ΓL(1,𝔽8) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #11763981 |
| commutator, hypocenter | C7×C13 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C72×C13 | C3×C4 |
| LCS | G ▷ C7×C13 | |
| UCS | C1 ◁ C7 | |
60 conjugacy classes of subgroups.
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7644, 162);