Finite Group DatabasebetaFinite Group Databasebeta| order | 5586 |
| isoclinism | isoclinic class of C19⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C2×C72×C19⋊C3 |
| unambiguous semidirect product | (C2×C19)⋊(C3×C72) |
| Fitting, socle, Hall | C2×C72×C19 ⋊ C3 |
| derived, Sylow | C19 ⋊ C2×C3×C72 |
| Hall | C72×C19 ⋊ C2×C3 |
| Hall | C2×C19 ⋊ C3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C72 | C19⋊C3 |
| commutator, hypocenter | C19 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C19 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C72 | |
80 conjugacy classes of subgroups.
882 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5586, 81);