Finite Group DatabasebetaFinite Group Databasebeta| order | 7956 |
| isoclinism | isoclinic class of AGL(1,𝔽13) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#261⋊C9 |
| unambiguous semidirect product | #261⋊(C9×C17) |
| unambiguous semidirect product | (C17×#261)⋊C9 |
| derived, Sylow | C13 ⋊ C4×C9×C17 |
| Hall | C17×C13⋊C9 ⋊ C4 |
| Hall | C17×#261 ⋊ C9 |
| Hall | C13×C17 ⋊ C4×C9 |
| Hall | C13⋊C9 ⋊ C4×C17 |
| Hall | #261 ⋊ C9×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C17 | AGL(1,𝔽13) |
| commutator, hypocenter | C13 | C4×C9×C17 |
| Frattini | C3 | C17×AGL(1,𝔽13) |
| Fitting, socle | C3×C13×C17 | C3×C4 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C17 | |
36 conjugacy classes of subgroups.
663 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7956, 14);