Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C19⋊C3)⋊D49 |
| Fitting, derived, Hall | C19×C49 ⋊ C2×C3 |
| Hall | C49×C19⋊C3 ⋊ C2 |
| Hall | D931 ⋊ C3 |
| Hall | C19⋊C3 ⋊ D49 |
| Sylow | C49 ⋊ D19⋊C3 |
| Sylow | C19 ⋊ C3×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C19×C49 | C2×C3 |
| Frattini | C7 | (C19⋊C3)⋊D7 |
| socle | C7×C19 | C3×D7 |
| LCS | G ▷ C19×C49 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,7,19,7|c^7=e^6,c^a=c^6e,d^a=d^18,e^a=e^6,d^b=d^7225 conjugacy classes — view the full character table.
| maximal subgroup of | D49×D19⋊C3, C2×(C19⋊C3)⋊D49, #30660500, … |
| maximal normal subgroup of | D49×D19⋊C3, C2×(C19⋊C3)⋊D49, #30660500, … |
| maximal quotient of | (C19⋊C3)⋊Dic49, C2×(C19⋊C3)⋊D49, #4294⋊D49, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 4);