Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C7 |
| unambiguous semidirect product | D19⋊#3862 |
| Fitting, socle, derived, Hall | C72×C19 ⋊ C2×C3 |
| Hall | C19⋊#3862 ⋊ C2 |
| Hall | C72×D19 ⋊ C3 |
| Sylow | C72 ⋊ D19⋊C3 |
| Hall | D19 ⋊ #3862 |
| Sylow | C19 ⋊ C2×#3862 |
| 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|e^a=e^18,c^b=c^2,d^b=d^4,e^b=e^7185 conjugacy classes — view the full character table.
| maximal subgroup of | D19⋊#64425, #26013908, #26013909, … |
| maximal normal subgroup of | D19⋊#64425, #26013908, #26013909, … |
| maximal quotient of | Dic19⋊#3862, C2×D19⋊#3862, #30660602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 69);