Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | ΓL(1,𝔽8)⋊D133 |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C2×C3 |
| Hall | C7×C19×ΓL(1,𝔽8) ⋊ C2 |
| Hall | C7⋊D133 ⋊ C3 |
| Hall | C7×ΓL(1,𝔽8) ⋊ D19 |
| Sylow | C72 ⋊ C3×D19 |
| Sylow | C19 ⋊ ΓL(1,𝔽8)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C19 | C2×C3 |
| LCS | G ▷ C72×C19 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7^2,19|c^a=c^6,d^a=d^6,e^a=e^18,c^b=c^2337 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 65);