Finite Group DatabasebetaFinite Group Databasebeta| order | 8690 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊D79 |
| unambiguous semidirect product | C79⋊AGL(1,𝔽11) |
| unambiguous semidirect product | D869⋊C5 |
| Fitting, socle, derived, Hall | C11×C79 ⋊ C2×C5 |
| Hall | C11⋊C5×C79 ⋊ C2 |
| Hall | D869 ⋊ C5 |
| Sylow | C79 ⋊ AGL(1,𝔽11) |
| Hall | C11⋊C5 ⋊ D79 |
| Sylow | C11 ⋊ C5×D79 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C11×C79 | C2×C5 |
| LCS | G ▷ C11×C79 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,5,11,79|c^a=c^10,d^a=d^78,c^b=c^4284 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8690, 12);