Finite Group DatabasebetaFinite Group Databasebeta| order | 10564 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×Dic139 |
| unambiguous semidirect product | C139⋊(C4×C19) |
| derived, Sylow | C139 ⋊ C4×C19 |
| Hall | C19×C139 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C19 | D139 |
| commutator, hypocenter | C139 | C4×C19 |
| Frattini | C2 | C19×D139 |
| Fitting, socle, prime radical | C2×C19×C139 | C2 |
| cosocle | C2×C139 | C2×C19 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C2×C19 | |
12 conjugacy classes of subgroups.
2698 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C19×Dic139, C19×Dic417, C19×(C139⋊C3)⋊C4, … |
| maximal normal subgroup of | C3×C19×Dic139, C19×(C139⋊C3)⋊C4, C19⋊C3×Dic139, … |
| maximal quotient of | C3×C19×Dic139, C19×Dic417 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10564, 3);