Finite Group DatabasebetaFinite Group Databasebeta| order | 1976 |
| isoclinism | isoclinic class of D19 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C13 · Schur multiplier (H2) = C2 |
| direct product | C2×C13×Dic19 |
| unambiguous semidirect product | (C2×C19)⋊(C4×C13) |
| derived, Sylow | C19 ⋊ C2×C4×C13 |
| Hall | C13×C19 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C13 | D19 |
| commutator, hypocenter | C19 | C2×C4×C13 |
| Frattini | C2 | C2×C13×D19 |
| Fitting, socle, prime radical | C22×C13×C19 | C2 |
| cosocle | C2×C19 | C22×C13 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C22×C13 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1976 |
572 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1976, 17);