Finite Group DatabasebetaFinite Group Databasebeta| order | 3534 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D589 |
| Fitting, socle, Hall | C3×C19×C31 ⋊ C2 |
| derived, Hall | C19×C31 ⋊ C2×C3 |
| Hall | C3×C31 ⋊ D19 |
| Hall | C3×C19 ⋊ D31 |
| Sylow | C31 ⋊ C3×D19 |
| Sylow | C19 ⋊ C3×D31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D589 |
| commutator, cosocle, hypocenter | C19×C31 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C3×C19×C31 | C2 |
| LCS | G ▷ C19×C31 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1767 |
888 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×D589, C3×D2945, C3×C19⋊(D31⋊C5), … |
| maximal normal subgroup of | C3×C5×D589, C3×C19⋊(D31⋊C5), C3×C7×D589 |
| maximal quotient of | C3×C5×D589, C3×D2945, C3×C7×D589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3534, 8);