Finite Group DatabasebetaFinite Group Databasebeta| order | 836 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic19 |
| unambiguous semidirect product | C19⋊(C4×C11) |
| derived, Sylow | C19 ⋊ C4×C11 |
| Hall | C11×C19 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D19 |
| commutator, hypocenter | C19 | C4×C11 |
| Frattini | C2 | C11×D19 |
| Fitting, socle, prime radical | C2×C11×C19 | C2 |
| cosocle | C2×C19 | C2×C11 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 836 |
242 conjugacy classes — view the full character table.
| maximal subgroup of | D11×Dic19, D209⋊C4, #13131880, … |
| maximal normal subgroup of | D11×Dic19, D209⋊C4, #13131880, … |
| maximal quotient of | C11×C19⋊C8, C2×C11×Dic19, C3×C11×Dic19, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(836, 2);