Finite Group DatabasebetaFinite Group Databasebeta| order | 10412 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#10587739 |
| Fitting, socle, Hall | C19×C137 ⋊ C4 |
| derived, Sylow | C137 ⋊ C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | #10587739 |
| commutator, hypocenter | C137 | C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C19×C137 | C4 |
| prime radical | C19×D137 | C2 |
| cosocle | D137 | C2×C19 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C19 | |
12 conjugacy classes of subgroups.
722 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×#10587739, C3×C19×#10587739, C19×C3⋊#10587739 |
| maximal normal subgroup of | C19⋊C3×#10587739, C3×C19×#10587739 |
| maximal quotient of | C3×C19×#10587739, C19×C3⋊#10587739 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10412, 6);