Finite Group DatabasebetaFinite Group Databasebeta| order | 5673 |
| isoclinism | isoclinic class of C61⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C61⋊C3 |
| unambiguous semidirect product | C61⋊(C3×C31) |
| Fitting, socle, Hall | C31×C61 ⋊ C3 |
| derived, Sylow | C61 ⋊ C3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C61⋊C3 |
| commutator, hypocenter | C61 | C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C31×C61 | C3 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C31 | |
8 conjugacy classes of subgroups.
713 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C31×C61⋊C3, C31×D61⋊C3, D31×C61⋊C3, … |
| maximal normal subgroup of | C2×C31×C61⋊C3, C31×D61⋊C3, D31×C61⋊C3, … |
| maximal quotient of | C2×C31×C61⋊C3, C31×C61⋊C9, C3×C31×C61⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5673, 2);