Finite Group DatabasebetaFinite Group Databasebeta| order | 10412 |
| isoclinism | isoclinic class of D137 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C19 · Schur multiplier (H2) = C2 |
| direct product | C2×C19×D137 |
| unambiguous semidirect product | C137⋊(C22×C19) |
| unambiguous semidirect product | (C2×C137)⋊(C2×C19) |
| Fitting, socle | C2×C19×C137 ⋊ C2 |
| derived, Sylow | C137 ⋊ C22×C19 |
| Hall | C19×C137 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D137 |
| commutator, cosocle, hypocenter | C137 | C22×C19 |
| Frattini | C1 | G |
| Fitting, socle | C2×C19×C137 | C2 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C2×C19 | |
20 conjugacy classes of subgroups.
2660 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C19⋊C3×D137, D3×C19×D137, C2×C3×C19×D137, … |
| maximal normal subgroup of | C2×C19⋊C3×D137, C2×C3×C19×D137 |
| maximal quotient of | D3×C19×D137, C2×C3×C19×D137, C2×C19×D411 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10412, 11);