Finite Group DatabasebetaFinite Group Databasebeta| order | 836 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C11 · Schur multiplier (H2) = C2 |
| direct product | C2×C11×D19 |
| unambiguous semidirect product | C19⋊(C22×C11) |
| unambiguous semidirect product | (C2×C19)⋊(C2×C11) |
| Fitting, socle | C2×C11×C19 ⋊ C2 |
| derived, Sylow | C19 ⋊ C22×C11 |
| Hall | C11×C19 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D19 |
| commutator, cosocle, hypocenter | C19 | C22×C11 |
| Frattini | C1 | G |
| Fitting, socle | C2×C11×C19 | C2 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C2×C11 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 418 |
242 conjugacy classes — view the full character table.
| maximal subgroup of | D19×Dic11, #13131878, #13131879, … |
| maximal normal subgroup of | D19×Dic11, #13131878, #13131879, … |
| maximal quotient of | C11×Dic38, C4×C11×D19, C11×D76, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(836, 6);